How many bits in the resultant hash will change, if the x bits are changed in its the original input?
For any one of the SHA hashes, the hash should be indistinguishable from pseudo-random. That means each and every bit flips with a chance of 50%. So on average half of the amount of bits gets flipped, as long as the input message doesn't repeat (because that will match 100% with the hash of the identical message, of course). It doesn't matter how many input bits are removed, added or altered, this is always the case as long as the input message isn't identical to the previous one.

Hashes are likely well distributed, so the likely number of bits that get flipped is a bell curve like you would get by throwing dice. Same thing for the number of zero bits - or one bits of course. So you cannot give an absolute number as an answer to this question. The result is not a function on $x$ if $x$ is the number of bits flipped in the input - as long as $x$ is larger than zero.