Randomness and reversibility of a sequence generated by taking sha256 hashes of an predictably-changing input?
This is basically how KDF1 and KDF2 work: use a secret, add a (constant sized) label + possible other values such as a salt and then use this as input for a hash value.

Another way to look at it is to view the seed + number as a new number and then reduce the problem to the problem that Richie Frame pointed at.

So:


yes it will behave randomly
no, no information about the seed can be retrieved
truncation of hashes is a well known method, and will not leak any more information