Sorry if this has already been asked i didnt find it in the forums. If I have 1 ready character left and I flip up finishing move can my opponent use puppet master in response thus fizzling my finishing move??

no

Yes, he can use Puppet Master but it won't affect your ability to play Finishing Move. Here's why:

Finishing Move states "As an additonal cost to play Finishing Move, exhaust a character you control."

Costs are paid upon announcement and cannot be responded to or interfered with.

This means by the time Puppet Master's power resolves, your character is already exhausted.

Cool, nother question.

I read that starting with the player with priority, players choose 1 stunned char to recover. After that point and both players have chosen. Can I use Negative Zone to stun the KO the chosen char?

No. Here's why:

No player receives priority during the recovery phase so no player has the opportunity to generate effects.

Your last opportunity to do so is at the start of the recovery phase, before anyone has chosen which character to recover.