Method of Salaah

Doubts in Surah Faatiha

Q: In my 'Asr Salaah I recited a verse of Surah Faatihah and whilst reciting I thought I made a mistake, and thought I'd repeat that verse and I didn't
stop reciting until I finished the verse, and then I recited again, but during the verse in which I thought I made a mistake, I was like “Shouldn't I stop?" But I carried on until finishing that verse; now I wonder, does this count as a purpose addition in prayer by finishing the verse in which I thought to have made a mistake? And is my Salaah valid?

Performing one rakaat

Q: First rakat of ishaa I said 'Ar-Rahman Ar-Raheem' but then I don't know whether I said the ha or HA with 'Ar-Raheeem'. I chose to ignore it as a doubt. During Salah I made many mistakes and corrections in the essential aspects - then after completing the prayer [all four rakaats] I ended prayer and did two sujood uh sahw. I went downstairs to get a drink, came back up then I still had the niggling doubt about whether I said ha or HA in 'Ar-Raheem' so I thought like you know it hasn't been a long time since I made Salaam so I said takbir and performed 1 rakaat in replacement of the rakaat in which I doubted with the full tashahhud and exited prayer and did two prostrations of forgetfulness Now plz tell me is my prayer valid or not?

Ijtimai Du'a and naseehat after Salaah

Q: After the Fardh Salah the Imam makes Du'a in which many if not the majority of people participate, arguably making it an Ijtimai Du'a. Thereafter, the Imam stands up and gives naseehat to the assembled congregation, thereby delaying the Sunnah prayer. From the end of Salah to the end of the naseehat is between 4-5min. It may be contended that nobody is obligated to sit for the naseehat. However when the majority, if not all the people sit for the nassehat, it makes it
awkward for one or a few individuals to depart to perform their Sunnah as:

(a) People are in the way and get inconvenienced.

(b) Persons draw uncomfortable attention to themselves by getting up and leaving.

Is delaying the Sunnah for this duration or at all permissible?

If not, what is the proof that such a delay is impermissible?