All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
First of all, it is important –dear brother –to know the pillars, the Waajibaat (obligations), and the desirable acts of the prayer and differentiate between them. Then, you need to know what can be made up by only the prostration for forgetfulness and what the prostration of forgetfulness is not sufficient for it.
None of what you mentioned in the question is included in the pillars of the prayer.
The raising of the hands in prayer is not a pillar but it is a desirable act. Similarly, sitting for the first Tashahhud is not a pillar, but rather, it is a Waajib that is compensated for by the prostration for forgetfulness if the praying person left it out forgetfully.
The legislated supplications in prayer are not a pillar as well, but some of them are Waajibaat, like the Tasbeeh in Rukoo’ (bowing down position) and Sujood (prostration) –according to some scholars –and some other supplications are desirable.
The pillars of the prayer are as follows:
1) Having the Intention.
2) Takbeeratul-Ihraam (the Takbeer for starting the prayer).
3) Standing when performing the (obligatory) prayer.
4) Reciting the Al-Faatihah (the Opening Chapter of the Quran)
6) Rising from Rukoo’.
8) Sitting between the two prostrations.
9) Sitting for the last Tashahhud.
10) Reciting the last Tashahhud.
11) The Ibraahimic supplication after it (i.e. after the Tashahhud).
12) Observing Tuma’neenah (being calm and feeling at ease) in all the above acts.
13) Saying Salaam (when concluding the prayer).
14) Observing the order (sequence) between the pillars.
Apart from these pillars, there are two categories:
2- The Sunan (recommended acts).
This categorization is the view of the Hanafi and Hanbali Schools of jurisprudence, but they have some differences in regard to the definition of some Waajibaat and Sunan. Hereunder is the view of the Hanbali School. The Waajibaat are:
1. The Takbeer when moving from one position to another at its proper place, which is between starting to move from one action to another, and finishing the movement.
2. Saying Sami’a Allaahu liman Hamidah (Allah answers the one who praises Him), while rising up from the Rukoo’. It is a Waajib on the Imam and the perosn praying individually, but not on the person praying behind the Imam.
3. Tahmeed: which is the saying: Rabbana walakal-hamdu (Our Lord, for You is all praise) after rising up from the Rukoo’. It is a Waajib on the Imam, the person praying behind the Imam, and the person praying individually.
4. Tasbeeh when in Rukoo’ position: which is the saying: Subhaana rabbiyal-‘Atheem (How perfect my Lord is, The Supreme).
5. Tasbeeh when in prostration, which is the saying: Subhaana rabbiyal-a’la (How perfect my Lord is, The Most High).
6. The saying: “Rabbigh-fir lee” (My Lord forgive me) when sitting between the two prostrations.
7. The first Tashahhud and sitting for it.
The difference between the pillar and the obligation in prayer is that if the worshiper abandons the pillar out of forgetfulness and then remembers it, he must (go back to its position and) perform it, and then prostrate for forgetfulness. As regards the Waajib, then he is not obliged to (go back to its position and) perform it if he had exceeded its place, and can he compensate for it by prostrating for forgetfulness.
As for the Sunan of the prayer, then these are all other actions other than the mentioned pillars and Waajibaat. A person does not have to prostrate for forgetfulness if he abandons it.
For more benefit, please refer to Fataawa 200531, 351019, 346423, 364543, raising his hands during the prayer ">89001 and 90330.
Allah knows best.