There is relation between Anapanasati and four Satipathanas.

ānāpānasati & the first satipaṭṭhāna "[1] Now, on whatever occasion a monk breathing in long discerns that he is breathing in long; or breathing out long, discerns that he is breathing out long; or breathing in short, discerns that he is breathing in short; or breathing out short, discerns that he is breathing out short; trains himself to breathe in... &... out sensitive to the entire body; trains himself to breathe in... &... out calming the bodily processes: On that occasion the monk remains focused on the body in & of itself — ardent, alert, & mindful — putting aside greed & distress with reference to the world. I tell you that this — the in-&-out breath — is classed as a body among bodies, which is why the monk on that occasion remains focused on the body in & of itself — ardent, alert, & mindful — putting aside greed & distress with reference to the world.

https://discourse.suttacentral.net/t/what-is-the-difference-between-satipa-hana-and-anapanasati/4796/2

After the 1st triad in Anapanasati Sutta:

1. First Tetrad: Contemplation of the Body (kāya)
   1. Discerning the in and out breathing
   2. Discerning long or short breaths
   3. Experiencing the whole body (sabbakāaya)
   4. Calming bodily formations

In the Maha Satipatthana Sutta other forms a Body Contemplations are mentioned.

"There are in this body

(1) the earth-element,

(2) the water-element,

(3) the fire-element,

(4) the air-element."

So build up until the 1st triad of breath meditation and switch to the 4 elements meditation. (Dhātu Vibhaṅga Sutta mentions 6 elements.)

Elaborating all the stages of breath meditation in this format is difficult. Best is to read: ANAPANASATI - MINDFULNESS WITH BREATHING: Unveiling the Secrets of Life: a Manual for Serious Beginners by BUDDHADASA BHIKKHU.

Awareness of the breath is also to establish mindfulness and there is a lot of overlap hence you want to read on this subject also: The Satipaṭṭhāna Suttas: An introduction by Piya Tan and also Satipaṭṭhāna, the Direct Path to Realization by Bhikkhu Analayo. Again is is very long to give it as an answer here.

Also Ven. Pa Auk Sayadaw teaches mindfulness of breath followed by 4 elements meditation. More on this see: Mindfulness of Breathing and Four Elements Meditation by Venerable Pa-Auk Sayadaw and Knowing and Seeing by Venerable Pa-Auk Sayadaw.

Q2. Also, can I know the simple explanation of what these actually mean

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I will breathe in calming bodily fabrication.

This is a mistranslation. It should be 'body fabricator'. The body fabricator is defined in MN 44 as the in & out breathing.

The breathing is the body fabricator because when the breathing is calm, the body is calm; if the breathing is agitated, the body is stressed.; if the breathing is unhealthy, the body is unhealthy. If the breathing ends, the body dies. If the breathing starts, the body lives.

This calming the breathing is achieved by having a quiet non-attached mind, which unifies itself with the breathing.

I will breathe in sensitive to rapture.

When the breathing & body calm sufficiently, rapture will arise to be the predominant object of meditation. It generally takes at least 60 to 75 minutes of calming the breathing constantly for rapture to arise.

Remember, the mind must be non-attached & in the present moment rather than craving for results & thinking about the future.

I will breathe in sensitive to pleasure.

If the mind remains non-attached & concentrated, the rapture will calm and pleasure or happiness will appear, which is a more refined pleasant feeling than rapture. Rapture (piti) is very vibrant, bubbly, agitating & seductive where as happiness (sukha) is more subtle, calm & soothing.

I will breathe in sensitive to mental fabrication

This again is a mistranslation. It should be 'mind fabricator'. Rapture & happiness are the mind fabricator (citta sankhara) because they seduce the mind and, if the mind is not mindful, rapture & happiness will fabricate craving, greed, love, attachment in the mind. This is why they are called the mind fabricator because they fabricate or condition defilment in the mind.

I will breathe in calming mental fabrication.

Just like when the breathing is calmed, by remaining non-attached & equanimous towards rapture & happiness, they will calm.

I will breathe in sensitive to the mind.

When rapture & happiness cease, the mind-heart (citta) itself becomes the object of meditation. Here, the mind has concentration. The mind is not thinking.

However, there will be some residual defilements in the mind such as greed, anger & confusion that subtly arose in response to the rapture. For example, sometimes the mind does not like rapture because the rapture disturbed the mind when it was peacefully watching breathing.

At stage 9, any residual defilements (kilesa) of the mind are observed & calmed.

I will breathe in satisfying the mind

When the defilements are calmed, the mind feels joy due to the cleansing of the defilements. This joy are more refined & subtle than rapture & happiness because the mind is now much more pure.

I will breathe in steadying the mind

When the joy calms, the mind concentrates deeply, in a one-pointed manner because it is pure.

I will breathe in releasing the mind

The mind (automatically) purifies itself of the one-pointedness of concentration & becomes open, bright & perfectly non-attached.

I will breathe in focusing on inconstancy.

At the previous stage the mind became liberated, open & non-attached.

Now, the impermanence of whatever subtle sense objects come to the mind is seen very clearly.

Here, the impermanence is so predominant that the mind sees mostly impermanence (rather than specific objects of impermanence). It is like watching a movie at very fast speed.

I will breathe in focusing on dispassion.

In seeing the crazy impermanence, craving is destroyed more because the impermanence makes sense objects look ugly, unattractive & undesirable.

I will breathe in focusing on cessation.

As craving is crushed or suspended, a taste of nirodha/Nibbana/no suffering/perfect peace occurs.

I will breathe in focusing on relinquishment.

The mind now fully knows all the experiences & things are not-self. It gives up holding anything as self.

The above is the fulfillment of stream-entry on the level of neighbourhood concentration. It is not jhana. It might take a few continuous meditation retreats to achieve this if the mind has no hindrances because reaching stage 9 in a very clear way can be difficult. However, one meditation retreat should be enough to reach stage 8 (if there are no hindrances).

Reading here: Buddhadasa: Mindfulness With Breathing Secrets of Life