Is it necessary to study Abhidhamma?

From a purely Theravada perspective,

1. Basic Abhidhamma is necessary to interpret Suttas. It is the primary usage.
2. If one didn't learn the basic Abhdhamma, he would interpret the Suttas in the wrong way and it would lead to wrong views.
3. The analysis of Abhidhamma doesn't allow any wrong view to arise.
4. If one doesn't learn basic Abhidhamma, he will most probably trap in a subtle "permanent entity" or "comfortable entity" or "self entity" in the world.
5. The well-analyzed nature of Abhidhamma keep the student away from such dangers. This is the major advantage.

Look for the beginning of the Dhammasangani Atthakata for reference.

Non of the Arahats, non of those gained path, fruit in the past, present, future, did study, study, would study literary Abhidhamma to gain path and fruits. Yet, non of those who seeked, seek, are up to seek fruits and path by means of study literary Abhidhamma, as the very means for it, have, do, or will gain path, fruit. Why is that? Because the path requires right view as base and the understanding of the practice, both hard to trace in literaly Abhidhamma, where such as path and Vimutti can hardly be found. Why is that: because literary Abhidhamma suggests "a" stand, views, beside of required right view. Abhidhamma's arising has it's causes, gained by doing the right path, doing. May one, falling out of the stated, correct the stated if wrong.

You asked "Is the knowledge of Sutta Pitaka enough to realize nirvana?" The problem here is that Pali canon contains two layers of suttas. An Early version closer to Buddha and a later version compiled by abhidhammikas. Latter is infused with ideas of the elders and their methods of meditation that contradict the original teachings. Hence, contradictions exist in the Pali canon, which might confuse the naive reader. If you have the time to read "Studies in Abhidhamma literature and the origins of Buddhist phiilosophical systems" by Erich Frauwallner then you will be in a better place to approach the Pali canon, and create a pathway to Nibbana. Sincerely,

If the Abhidhamma, such as the Paṭiccasamuppādavibhaṅga & Saccavibhaṅga, is actually read, it openly offers a different explanation to the Suttas. This appears obviously why many well-read Buddhists ignore the Abhidhamma.

Short answer on Abhidhamma is no. Not only is it not necessary, it is advisable to be avoided and it has no practical application. All it can offer is a form of pseudo-intellectual entertainment.

Short answer on Sutta Pitaka is yes. A few select chapters represent the essence of the teaching of the Enlightened One. When put to practice, they bring about the eradication of suffering.

From a purely Theravada perspective, how much important is it to read and know Abhidhamma? Is the knowledge of Sutta Pitaka enough to realize nirvana?

With all due consideration,

In order to accurately understand the response, one needs to clarify what is understood by knowledge. If it refers to reading, reciting, or discussing any text, discourse or instruction, no such conditioned type of knowledge will ever lead to liberation from suffering, or Nibbana. Only if it refers to the unconditional knowledge of truth, which can stem only from the practical application of any instruction, thus truly knowing said instruction to be accurate or not, then the essence of knowledge from a purely old school Theravadin perspective is to acknowledge that, truthfully, “this is suffering”, “this is the origin of suffering”, “this is the eradication of suffering”, “this is the path that progresses towards the eradication of suffering”.

Bearing this in mind, a thorough and exhaustive study of the Sutta Pitaka is more than enough for understanding the four noble expressions of the truth about suffering and for applying them in order to progress towards the unconditioned and perfectly liberated state of Nibbana. What could prove even more useful for such an endeavor is the reading of at least the key elements of the doctrine in the original Pali, so as not to be confused by the several and at times imprecise variations of translations.

One who might have read the entire Sutta Pitaka and who might have taken up Pali courses for precisely this purpose could tell that especially for the key notions of the doctrine, it is very rarely possible to translate them word by word. For now, only reading them in Pali and using as a filter the direct practical application of the perfectly enlightened one's teachings can help one understand their occurrence in the different expositions and the relationship between different terms that make up the core of the doctrine.

All-in-all, reading any text or commentary that revolves around the developing of mindfulness or the noble eightfold path can prove useful for a more thorough understanding of the terminology, mainly in the original dialect. But, just as reading about food does not quench hunger, nor does talking about water quench thirst, although it is useful to gain a theoretical understanding of the instructions for the attainment of Nibbana, in order for them to quench suffering, practical application is crucial.

Respectfully

Abhidhamma is inside of a person who fulfilled perfection of wholesome, Parami. A person who seeing the fastest-of-trillion-thousand-arising-and-vanishing-mind-moments-per-second is a person who understood abhidhamma.

It's hard for a foolish one who has no perfection of wholesome and wisdom. But it Tipitaka there are many people who have fulfilled perfection of wholesome, so it looks like easy to enlighten in Tipitaka when one just read, not memorize Tipitaka Pali.

So, the question is something like making an unequal person to be equal such as "Is it important for Albert Einstein to learn physic to understand the Theory of relativity" and "Is it important for a normal person to learn physic to understand the Theory of relativity".

Remember whether one important reason to meditate Jhana is because of the hardness of the insight meditation. The practitioner's wholesome need to be perfect enough, by Jhana, to study the hardest part of wisdom, the insight meditation. It is not only Abhidhamma, but it is seeing Abhidhamma in the past lives and the next lives until enlightenment like the Buddha did in his enlightening night.

Science is hard because of it's detail, the Dhamma is hard because it included all sciences as a little part of the whole Dhamma, Abhidhamma.

However, practice Jhana before study Abhidhamma. And it is very important to study Abhidhamma whith Jana-Mastery who memorized entired Tipitaka. The practitioner don't know who is Jhana-mastery without meditate by himself.

The traditional Theravada view is that the Abhidhamma was taught by the Buddha himself and traditionalists view it as "advanced Dhamma".

But modern academic scholarship and monk-scholars like Ven. Bodhi and Ven. Analayo (from this answer) say that Abhidhamma means "about the Dhamma" or "analysis of the Dhamma" and it's basically a body of work that evolved over the centuries based on discussions by monks of the sangha, and serves to provide additional explanation on the Dhamma taught by the Buddha himself.

On the other hand, the Buddha stated that he has taught everything necessary for liberation, for example, in the Simsapa Sutta. There's no absolute need for sutta commentaries and the Abhidhamma.

However, traditional sutta commentaries and the Abhidhamma are useful for improving our understanding of the Dhamma as taught by the Buddha. The traditional sutta commentaries provide context for the suttas (for e.g. the Dhammapada stories), or explain some cryptic statements (for e.g. this question).

The Abhidhamma provides meta-explanations or study guides on the sutta contents for e.g. explaining perception (saññā) as being related to memory, the enumeration of various mind states like wholesome mind states, unwholesome mind states etc. It also formalizes the concept of mind-moments and the linking of mind-moments.

So, in conclusion, the Abhidhamma should be treated as an optional study guide on the suttas.

Also, as explained in this answer, the main suttas are mostly common between different schools, but the Abhidhamma or Abhidharma, being a later work, is highly divergent between different schools.

If you enjoy beating your head against a brick wall, then abhidhamma might be for you. Abhidhamma came a hundred years or so after the Buddha died. If the Buddha thought it was important and worthwhile to teach the general public, he would have done so. If proponents of Abhidhamma are trying to tell you the Buddha secretly taught it to only his advanced students, you should be suspicious. In the suttas, the Buddha said there was no secret teachings he was hiding.

1st Q:

Is the knowledge of Sutta Pitaka enough to realize nirvana?

For some people even the gist is enough

Then Sariputta the wanderer spoke thus to the Ven. Assaji:

Speak a little or a lot, but tell me just the gist. The gist is what I want. What use is a lot of verbosity? Then Ven. Assaji gave this Dhamma exposition to Sariputta the Wanderer:

Whatever phenomena arise from cause: their cause & their cessation. Such is the teaching of the Tathagata, the Great Contemplative.

Then to Sariputta the wanderer, as he heard this Dhamma exposition, there arose the dustless, stainless Dhamma eye: "Whatever is subject to origination is all subject to cessation."

Even if just this is the Dhamma, you have penetrated to the Sorrowless (asoka) State unseen, overlooked (by us) for many myriads of aeons. Upatissa-pasine: Upatissa's (Sariputta's) Question

For some a discourse is enough, for some two discourses and for others thousands won't do.

Some people are just too dull

An6.87. Kamma Obstructions “Endowed with these six qualities, a person is incapable of alighting on the lawfulness, the rightness of skillful mental qualities even when listening to the true Dhamma. Which six?

“He has killed his mother; he has killed his father; he has killed an arahant; he has, with corrupt intent, caused the blood of a Tathagata to flow; he has caused a split in the Sangha; or he is a person of dull discernment, slow & dull-witted.

Whereas others are too invested in thinking otherwise

But this generation delights in attachment, is excited by attachment, enjoys attachment. For a generation delighting in attachment, excited by attachment, enjoying attachment, this/that conditionality and dependent co-arising are hard to see. This state, too, is hard to see: the resolution of all fabrications, the relinquishment of all acquisitions, the ending of craving; dispassion; cessation; Unbinding. Ayacana Sutta: The Request

“No wonder you don’t understand, Vaccha, no wonder you’re confused. For this principle is deep, hard to see, hard to understand, peaceful, sublime, beyond the scope of logic, subtle, comprehensible to the astute. It’s hard for you to understand, since you have a different view, creed, preference, practice, and tradition.With Vacchagotta on Fire

People are generally afraid of non-existence and are delighting in existence, which prevents them from understanding how to give up the wrong views in regards to existence & non existence

(8) “Bhikkhus, of the speculative views held by outsiders, this is the foremost, namely: ‘I might not be and it might not be mine; I shall not be, and it will not be mine.’ For it can be expected that one who holds such a view will not be unrepelled by existence and will not be repelled by the cessation of existence. 10.29. Kosala (1)

"The world in general, Kaccaayana, inclines to two views, to existence[2] or to non-existence.[3] But for him who, with the highest wisdom, sees the uprising of the world as it really is,[4] 'non-existence of the world' does not apply, and for him who, with highest wisdom, sees the passing away of the world as it really is, 'existence of the world' does not apply. SN 12.15 Kaccayanagotta Sutta: To Kaccayana Gotta (on Right View)

Of course meditation is the way to overcome this but people don't generally want to go

9.414.With the Householder Tapussa

“Sir, Ānanda, we are laypeople who enjoy sensual pleasures. We like sensual pleasures, we love them and take joy in them. But renunciation seems like an abyss. I have heard that in this teaching and training there are very young mendicants whose minds are eager for renunciation; they’re confident, settled, and decided about it. They see it as peaceful. Renunciation is the dividing line between the multitude and the mendicants in this teaching and training.”

“Householder, we should see the Buddha about this matter. Come, let’s go to the Buddha and inform him about this. As he answers, so we’ll remember it.”

“Yes, sir,” replied Tapussa. Then Ānanda together with Tapussa went to the Buddha, bowed, and sat down to one side. Ānanda told him what had happened.

“That’s so true, Ānanda! That’s so true! Before my awakening—when I was still unawakened but intent on awakening—I too thought, ‘Renunciation is good! Seclusion is good!’ But my mind wasn’t eager for renunciation; it wasn’t confident, settled, and decided about it. I didn’t see it as peaceful. Then I thought, ‘What is the cause, what is the reason why my mind isn’t eager for renunciation, and not confident, settled, and decided about it? Why don’t I see it as peaceful?’ Then I thought, ‘I haven’t seen the drawbacks of sensual pleasures, and so I haven’t cultivated that. I haven’t realized the benefits of renunciation, and so I haven’t developed that. That’s why my mind isn’t eager for renunciation, and not confident, settled, and decided about it. And it’s why I don’t see it as peaceful.’ 

2nd Q:

From a purely Theravada perspective, how much important is it to read and know Abhidhamma?

I am not an expert on Theravadin Abhidhamma, merely familiar with it, and would want to compare it to the Sarvastivadin Abhidhamma before i can give a real educated answer but i'll share my thoughts.

It is my impression so far that it's main utility & value is two-fold:

1. Cross-referencing with Sutta, that might be a great way to study both in tandem.

2. 'Interrogation' for the purpose of conformity, preventing people from saying wrong things.