If someone uses search and destroy on my charaxes or any arkham character, and then i play blackgate prison to stun my arkham inmate at a cost of three or less, do i still have to discard any copies of that same character from my hand? I don't believe i have to only because I was the one who stunned my arkham character and not search and destroy, but i still have to show my hand. If that is incorrect, someone please help me clear this up.

Search and Destroy
Plot Twist, 3
As an additional cost to play Search and Destroy, stun a ready army Sentinel character you control.
Stun target character with a cost of 3 or less. That character's controller reveals his hand and discards all character cards of the same name.

The effect does not care if it succesfully stuns the character, it tries to stun it, then you still have to do the second part. You can even play this on an already stunned character if you want to make them discard.

Search And Destroy:
The discard is not dependent upon the stun.

The only way to put a stop to S&D is to negate it.