1. You haven't, that's just it. It could be a DWORD, long, even an [un]signed integer larger or smaller than 32-bits. Or it could even be a float or double. In that case, what if I just assume it's a standard 32-bit integer and try to do a bitwise operation on it?1. No, but I have yet to encounter a case where a "count" of something is anything other than an integer type of some sort. Redundant information is not useful
2. The word "count" doesn't tell you much right off the bat, except what it's used for.
1. Why are you doing bitwise operations on a counter variable? A counter is something that counts. If you're going to do further operations on a counter then it has effectively ceased to be a counter and has become something else, in which case you should just create another variable or rename the old one with a name that better reflects what you're actually doing.
To be totally fair, I actually have seen this done.
On much older platforms, like the NES, some games perform bitwise operations on the global frame counter to control background animations.