I can feel the rising and falling of sensations in vipassana, but what to make of thoughts?

Thoughts are result in verbal fabrications which result in sensations, when the thought makes contact with the mind sense door.

Each time a thought arises there is an associated sensation through out the body. If you have many successive such thoughts this sensation accumulates. E.g. multiple depressing thoughts will leave you depressed. Happy memories will leave you happy and smiling.

Main few things you actively do:

1. Calm down the verbal and metal fabrications by trying to bring your wondering mind to a chosen object
2. Look at the sensation in the body (mainly around your head) the thought proliferation has created. (Tightness, heaviness, depressed, happy, excited, passionate, etc. - also if you look deeply these are combinations of the Elements) due to thoughts. This will calm any bodily fabrications. Also pay attention to changes in breathing. If breathing becomes fast. If breathing has stopped does it start again. Also you pulse.
3. Identify if the sensation is due to a mental reaction due to perception and see perception creates misery also and dilute these perceptions.

But if the thoughts are too strong and persist, I tend to observe them impartially until they leave of their own accord (but during this time my observance of anicca has stopped). Am I doing this thing rightly or not?

Your observance of anicca should not stop.

Secondly, I want to understand the reality of thoughts. I know that ultimately none of these have permanent reality, but compared to conditioned reality of sensations what is the conditioned reality of thoughts?

You should answer your question yourself. Wisdom gained through experience is the right path to liberation. If you want to know what is the conditioned reality of thoughts, do this:

1. Mindfully observe your thoughts arising and ceasing until they leave of their own accord.

2. Do step 1 until you mindfully observe: "There are no thoughts arising in me". Once you note that your mind is completely stilled, proceed to the next step.

3. Mindfully and slowly arise a thought, for example arise a visualization of an object. Observe how the thought visualization of the object arises. Then, mindfully and slowly let go of this same thought visualization of the object. Observe how the thought visualization of the object ceases. Repeat the process. The key here is mindfulness.

Like an experienced forensic who is dissecting every inch of a crime scene, so should you dissect your mind when a thought arises and ceases.

By doing the above exercise and mindfully observing what happens in step 3, you will understand the reality of thoughts. You will see why they arise. You will see why they cease.

Here is a video called "Ask A Monk: Correct Observation of Thoughts" by Ven. Yuttadhammo.

In here its talked about how to observe thoughts and also about what happens when one is forcing thoughts to go away or to trying to stop thinking. You might this video useful.

There is also a short quote on how to deal with thoughts from the book "How To Meditate: A Beginner's Guide to Peace" by Ven. Yuttadhammo, p. 11:

"...In regards to the mind, if thoughts arise during meditation, one should acknowledge them as “thinking”. It doesn't matter whether one is thinking about the past or future or whether one's thoughts are good or bad; instead of letting the mind wander and lose track of reality, bring the mind back to the reality of the thought with, "thinking". Then return to the rising and falling and continue practice as normal..."

How should I treat thoughts?

You should strive to know thoughts as thoughts. If you are observing impartially, that's good. If you are ignoring the light, fleeting thoughts, it depends what you mean. You don't want to actively ignore anything as that will cultivate aversion or even a dullness of mind. If you mean the thoughts are just too light, too fleeting to catch, then you're doing what you can, and your coverage will improve with practice, if you strive for it.

The other side of this is that it's more important to impartially observe whatever comes up, rather than simply impartially observing thoughts. That is, you should try to stay in the here and the now. A thought might become frustration, and you should observe that impartially. Then the frustration becomes hotness in the body. As soon as we are aware of the hotness, we should observe the hotness. Or perhaps coldness following fear. And then maybe the thought comes back, and we observe that, or we feel an irritation on the skin, and we observe that. I'm giving as many examples as I can from my own experience to try to illustrate that when a thought overtakes us, the here-and-now can be a swiftly-moving target.

What is the conditioned reality of thoughts?

The Buddha placed thoughts on an equal footing with all other sensations, as you can read in the very brief Sabba Sutta (found in the Samyutta Nikaya, Sutta #35.23):

"Monks, I will teach you the All. Listen & pay close attention. I will speak."

"As you say, lord," the monks responded.

The Blessed One said, "What is the All? Simply the eye & forms, ear & sounds, nose & aromas, tongue & flavors, body & tactile sensations, intellect & ideas. This, monks, is called the All. Anyone who would say, 'Repudiating this All, I will describe another,' if questioned on what exactly might be the grounds for his statement, would be unable to explain, and furthermore, would be put to grief. Why? Because it lies beyond range."

So from a meditative point of view, the most objective things you have are the thoughts and the senses. Don't worry too much whether thoughts are objective or subjective. Rather consider objectively that a thought is a thought, and seeing it as anything else is subjective.