Obligatory Parts and Sunnah Acts of Prayer
Question

Would you, please, shed some light on the pillars, obligatory parts and sunnah acts of prayer?
Praise be to Allah.Sunnah acts of prayer
There are many Sunnahs of prayer, both words and actions. What is meant by Sunnahs is things other than the pillars (essential parts) and obligatory parts of the prayer. 
Some of the fuqaha’ stated that there are seventeen verbal Sunnahs in prayer, and fifty-five actions which are Sunnah. The prayer is not invalidated if one omits one of these actions, even if that is done deliberately, unlike the pillars and obligatory parts. 
The difference between a pillar and an obligatory part is that a pillar cannot be waived, whether one omits it deliberately or by mistake, rather it must be done. An obligatory part is waived if one forgets, and it can be compensated for by doing the prostration of forgetfulness (sujood al-sahw). 
It may be useful here to mention the pillars of prayer and its obligatory parts, followed by some of its Sunnahs, based on the book Daleel al-Taalib, which is a well known summary used by Hanbali fuqaha’.
Pillars of prayer
There are 14 pillars of prayer which are as follows:
(1) Standing during obligatory prayers if one is able to do so
(2) The opening takbeer (saying “Allahu akbar”)
(3) Reciting al-Faatihah
(4) Rukoo’ (bowing), the least of which means bending so that the hands can touch the knees, but the most complete form means making the back level and the head parallel with it.
(5) Rising from bowing
(6) Standing up straight
(7) Sujood (prostration), the most perfect form of which is placing the forehead, nose, palms, knees and toes firmly on the ground, and the least of which is placing a part of each of these on the ground.
(8) Rising from prostration
(9) Sitting between the two prostrations. However one sits is good enough, but the Sunnah is to sit muftarishan, which means sitting on the left foot and holding the right foot upright with the toes pointing towards the qiblah.
(10) Being at ease in each of these physical pillars
(11) The final tashahhud
(12) Sitting to recite the final tashahhud and the two salaams
(13) The two salaams. This means saying twice, “al-salaamu ‘alaykum wa rahmat-Allah (Peace be upon you and the mercy of Allah).” In naafil prayers it is sufficient to say one salaam; the same also applies to the funeral prayer.
(14) Doing the pillars in the order mentioned here. If a person deliberately prostrates before bowing, for example, the prayer is invalidated; if he does that by mistake, he has to go back and bow, and then prostrate.
Obligatory parts of prayer
The obligatory parts of prayer are eight, which are as follows:
(1) Takbeers other than the opening takbeer
(2) Saying “Sami’a Allahu liman hamidah (Allah hears those who praise Him” – for the imam and for the one who is praying alone.
(3) Saying “Rabbana wa laka’l-hamd (Our Lord, to You be praise)”
(4) Saying “Subhaana rabbiy al-‘azeem (Glory be to my Lord Almighty)” once when bowing
(5) Saying “Subhaana rabbiy al-a’laa (Glory be to my Lord most High)” once when prostrating
(6) Saying “Rabb ighfir li (Lord forgive me)” between the two prostrations
(7)The first tashahhud
(8) Sitting for the first tashahhud
Verbal Sunnahs of prayer
The verbal Sunnahs are eleven, which are as follows:
 (1) Saying after the opening takbeer, “Subhaanaka Allahumma wa bi hamdika, wa tabaaraka ismuka, wa ta’aala jadduka wa laa ilaaha ghayruka (Glory and praise be to You, O Allah; blessed be Your name, exalted be Your Majesty, and there is no god but You).” This is called du’aa’ al-istiftaah (opening du’aa’)
(2) Seeking refuge with Allah
(3) Saying Bismillaah
(4) Saying Ameen
(5) Reciting a soorah after al-Faatihah
(6) Reciting out loud, in the case of the imam
(7) Saying after the tahmeed (Rabbana wa laka’l-hamd), for one who is not praying behind an imam: “Mil’ al-samawaati wa mil’ al-ard wa mil’ ma shi’ta min shay’in ba’d (Filling the heavens, filling the earth, and filling whatever else You wish).” (The correct view is that it is also Sunnah for one who is praying in congregation)
(8) Saying the tasbeeh when bowing more than once, such as a second or third time or more
(9) Saying the tasbeeh in prostration more than once
(10) Saying “Rabb ighfir li (Lord forgive me)” more than once between the two prostrations
(11) Sending prayers upon the family of the Prophet (peace and blessings of Allah be upon him) in the last tashahhud and sending blessings upon him and upon them, and saying du’aa’ after that.
Sunnah actions of prayer
The Sunnah actions are called postures. They are as follows:
(1) Raising the hands when saying the opening takbeer
(2) Raising the hands when bowing
(3) Raising the hands when rising from bowing
(4) Dropping them after that
(5) Placing the right hand over the left
(6) Looking towards the place of prostration
(7) Standing with the feet apart
(8) Holding the knees with fingers spread apart when bowing, holding the back straight and making the head parallel with it.
(9) Placing the parts of the body on which one prostrates firmly on the ground, apart from the knees, because it is makrooh to press them firmly on the ground.
(10) Keeping the elbows away from the sides, and the belly from the thighs, and the thighs from the calves; keeping the knees apart; holding the feet upright; holding the toes apart on the ground; placing the hands level with the shoulders with the fingers spread.
(11) Sitting muftarishan between the two prostrations and in the first tashahhud, and sitting mutawarrikan in the second tashahhud.
(12) Placing the hands on the thighs with the fingers together between the two prostrations, and in the tashahhud, except that in the latter the pinkie and ring fingers should be held in, a circle made with the middle finger and thumb, and one should point with the forefinger when remembering Allah.
(13) Turning to the right and left when saying the salaam
There are some differences of opinion among the fuqaha’ regarding some of these issues; what is regarded as obligatory by some is regarded as Sunnah by others. This is discussed in detail in the books of fiqh. 
And Allah knows best.