Firstly: 

Standing, bowing and prostrating are pillars or essential parts of the prayer. Whoever can do them, it is obligatory for him to do them in the manner prescribed in sharee’ah. Whoever is not able to do them because of sickness or old age, it is Sunnah for him to sit on the ground or on a chair. 

Allaah says (interpretation of the meaning): 

“Guard strictly (five obligatory) As‑Salawaat (the prayers) especially the middle Salaah (i.e. the best prayer ‑ ‘Asr). And stand before Allaah with obedience [and do not speak to others during the Salaah (prayers)]”

[al-Baqarah 2:238]

It was narrated that ‘Imraan ibn Husayn (may Allaah be pleased with him) said: I had haemorrhoids so I asked the Prophet (peace and blessings of Allaah be upon him) about praying. He said: “Pray standing up; if you cannot, then pray sitting down; and if you cannot, then pray (lying) on your side.” Narrated by al-Bukhaari, 1066. 

Ibn Qudaamah al-Maqdisi said: 

The scholars are unanimously agreed that if a person cannot stand then he may pray sitting down. Al-Mughni, 1/443 

Al-Nawawi said: 

The ummah is unanimously agreed that whoever is unable to stand during the obligatory prayer may pray sitting, and he does not have to repeat it. Our companions said: his reward will not be less than the reward for praying standing, because he is excused. It is proven in Saheeh al-Bukhaari that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “If a person is sick or travelling, the same reward will be written for him with regard to what he used to do when he was not travelling and was healthy.”

Al-Majmoo’, 4/226 

Al-Shawkaani said: 

The hadeeth of ‘Imraan indicates that it is permissible for one who has an excuse and cannot stand to pray sitting, and for one who has an excuse and cannot pray sitting to pray lying on his side.

Nayl al-Awtaar, 3/243 

Shaykh al-Islam Ibn Taymiyah said: 

The Muslims are agreed that if a worshipper is unable to do some of the obligatory duties of prayer, such as standing, reciting, bowing, prostrating, covering the ‘awrah, facing the qiblah etc, then what he is unable to do is waived for him. End quote from Majmoo’ al-Fataawa, 8/437 

Based on that, if a person offers an obligatory prayer sitting when he is able to stand, his prayer is invalid. 

Secondly: 

It should be noted that if a person is exempted from standing, his excuse does not make it permissible for him to sit on the chair to bow and prostrate. 

If he is exempted from bowing and prostrating in the proper manner, that excuse does not make it permissible for him not to stand and to sit on the chair instead. 

The basic principle with regard to the obligatory duties of prayer is that whatever the worshipper can do, he is obliged to do it, and whatever he is unable to do, is waived for him. 

Whoever is unable to stand, it is permissible for him to sit on a chair during the standing, and he should bow and prostrate in the proper manner. If he is able to stand but it is difficult for him to bow and prostrate, he should pray standing, then sit on the chair when bowing and prostrating, and he should bend lower for the prostration than for the bowing.  

See also question no. 9307 and 36738. 

Ibn Qudaamah al-Maqdisi said: 

If a person is able to stand but he cannot bow or prostrate, the standing is not waived for him; he should pray standing and tilt his head for the bowing, then sit down and tilt his head for the prostration. This is the view of al-Shaafa’i… 

Because Allaah says (interpretation of the meaning): “And stand before Allaah with obedience” [al-Baqarah 2:238], and the Prophet (peace and blessings of Allaah be upon him) said: “Pray standing.” And because standing is one of the pillars (essential parts of prayer) for the one who is able to do it, so he must do it, like the recitation. Being unable to do other things does not mean that this is waived, as is also the case if he is unable to recite. End quote from al-Mughni, 1/44. 

Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allaah have mercy on him) said: 

The one who prays sitting on the ground or on a chair must make his prostration lower than his bowing. The Sunnah is for him to put his hands on his knees when bowing, and when prostrating the Sunnah is to put them on the ground if possible; if he cannot do that then he should put them on his knees, because it was proven that the Prophet (peace and blessings of Allaah be upon him) said: “I have been commanded to prostrate on seven bones: the forehead – and he pointed to his nose – the two hands, the two knees, and the edges of the two feet (i.e., the toes).” 

If a person is unable to do that and prays on a chair, there is nothing wrong with that, because Allaah says (interpretation of the meaning): 

“So keep your duty to Allaah and fear Him as much as you can”

[al-Taghaabaun 64:16]

and the Prophet (peace and blessings of Allaah be upon him) said: “If I tell you to do a thing, then do as much of it as you can.” Saheeh – agreed upon. 

Fataawa Ibn Baaz, 12/245, 246. 

Thirdly: 

With regard to the placement of the chair in the row, the scholars (may Allaah have mercy on them) stated that the one who prays sitting down should have his posterior in line with the row when he is sitting, so he should not be in front of the row or behind it at that point, because that is the place in which the body settles. 

See Asnaa al-Mataalib, 1/222; Tuhfat al-Muhtaaj, 2/157; Sharh Muntaha al-Iraadaat, 1/279. 

It says in al-Mawsoo’ah al-Fiqhiyyah (6/21): 

In order for a person’s following the imam to be valid, he should not stand in front of the imam according to the majority of fuqaha’ (Hanafis, Shaafaa’is and Hanbalis). 

How do we know whether he is in front of the imam or not, it is judged by where the heels are. If they are standing level at the heel and the toes of the one who is praying behind the imam turn out to be in front because he has longer feet, that does not matter. With regard to those who are sitting, it is judged by where the posterior is. And with regard to those who are praying on their sides, it is judged by their sides.   

If the worshipper is going to pray on the chair from the beginning of the prayer until the end, then he should make the place where he will sit level with the row. 

If he is going to pray standing, but he will sit on the chair when he bows and prostrates, we asked Shaykh ‘Abd al-Rahmaan al-Barraak about that, and he said that what matters here is the standing position, so he should be level with the row when standing.  

Based on this, the chair will be behind the row, so it should be placed in such a manner that it will not disturb worshippers in the row behind. 

And Allaah knows best.