If there was actually some kind of burning in the HDD them it wouldn't be too surprising if your data was gone. But you could try data recovery services, there are some free ones.
The target load temperature for the RX 480 is 80℃ and the maximum safe temperature is 90℃. Perhaps you can make the card run at 80℃ at a lower fan speed, I think Afterburner allows you to manually change fan speed.
I don't believe that pushing down the notches will damage it, unless you have a large amount of space under your motherboard (long standoffs if such a thing exists) then it should be fine.