Answer 1

There are many methods to detect single bit error.
You can use hammings code which is useful for both detection and correction otherwise go for crc(cyclic redundancy check) method

Answer 2

This reminds me of error-detecting codes.
You have to disallow certain combinations of 1s and 0s, so if you receive one of those disallowed combinations, you would know there is an error.
Error-correcting codes would disallow enough combinations so that, if one of those bits were corrupted, it would know what it should have been. The trade-off is that you reduce the number of allowable combinations by a lot.

Answer 3

So you want to check if the 6th bit (counted from the right) is 1? You can do that with n & 32. Or is that not what you're trying to do?

Answer 4

Hashes (or checksums) . Many download sites provide a sha256 hash to verify data integrity.
On SpaceX rockets, where you have a lot of radiations from space, and thus a lot of bit flips, you basically have 3 computers doing the same thing in parallel. If one of them disagrees, but the other two agree, it is assumed that the other 2 are right.
There are many ways to avoid data corruption, as this is a decently large field of study in computer science.