Will my salah be invalidated if I send salam to prophet (s.a.w) if his name comes in the zammi surah? Or should I send salaam after salaah?
This may not fully answer your question, but it is recommended to recite the quran and interact with it. This means if you read a verse including a du'a in Quran you are allowed to say Ameen. If you read a verse about Allah's mercy you may ask Allah for his mercy and if you read a verse of punishment you may ask Allah for forgiveness etc.. it is recommended to say subhan Allah if you passed by a verse praising Allah like 87:1 etc.. But as I understood this this would be allowed if you did so in secret or alone.
As a follower behind an Imam that would imply that you are free to send Greetings or Salam to our beloved Prophet at least in secret. As an Imam I wouldn't recommend doing this as for example it is not allowed to say "balaa بلى" affirming and answering the Question after reciting 95:8 etc. because this statement is not part of the Quran, and some listeners might think it would be!
بلى means: certainly, truly, indeed in Arabic.