Can changing batteries a lot in a digital camera burn out a memory card or camera?

No. The internal memory of the camera is determined at the factory, the memory card can't lose available space, and the batteries obviously need to be changed every now and then.

no
it has no effect on those 2 things

i don't think so but you can call where you got it from

AAAAAAAAAAAAAHHHHHHHHHHHHHH NO!!! you will be fine!

Bob