All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
Standing in the obligatory prayers is one of the pillars of the prayer without which the prayer is void for a person who is able to stand. Allaah says (what means): {…and stand before Allaah, devoutly obedient.} [Quran 2:238]
Also, the Prophet said, “Pray standing, and if you are unable to do so, then pray sitting down, and if again you are unable to do so, then pray while (lying down) on your side.” [Al-Bukhari]
It is only the person who is unable to stand or who is sick and whose disease increases when he stands up who is exempted from standing in the prayer.
Ibn Qudaamah said, “If when a sick person stands up his disease increases, then he may pray while sitting down…”
Therefore, if you are able to pray while standing and bowing, as you mentioned, then you are obliged to do so [stand], and it is not permissible for you to pray while sitting down from the beginning of the prayer while you are able to stand.
An-Nawawi said, “If a person is unable to bow down and prostrate but is able to stand up because of an ailment in his back that prevents him from bending [for bowing or prostrating], then he must stand up and perform the bowing and prostration according to his ability; so he should lean forward with his back as much as possible, and if he cannot bear that, then he should lean forward with his neck and his head...”
Moreover, Ibn Qudaamah said, “If a person is able to stand up but is unable to bow down or prostrate, then he is not exempted from standing up, and he should pray while standing up, so he nods instead of bowing (with his head) and then sits down and nods with his head again for the prostration. This is the view of ash-Shafi’i...”
As regards the people whom you mentioned, that they pray while they are ahead of the row because of putting the back legs of the chair along with the row, then their prayer is valid. They should have been in the same line as the row when standing up; nevertheless, the chair should be placed where it does not cause any harm or disturbance to the worshipers praying behind him.
Allaah knows best.