@emre299 when you click on Burn Bootloader, you get these errors
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 1 of 10: not in sync: resp=0x03
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 2 of 10: not in sync: resp=0x03
So you verified the connections. Did you verify also with a multimeter? A wire can be broken internally
Do you have another pro mini to verify the connections?
I would try different settings like the normal settings 3.3V and 8Mzh externally, etc
If this does not work, I have no ideas anymore...