No. It doesn't have to be any specific genre. Although, you'd do best to tell us in the Topic what it is: MyStory (historic fiction) -- 5000 words, or the like. That way people can judge it in that way.
Yep, just specify. Most people here write sci-fi/fantasy of some sort or another, or have some type of speculative element to their work, so they are particularly well-suited to provide feedback within those genres since they read a ton of it too.
But be sure to tell us what genre your story is, and we'll <try to> act/critique appropriately. Just be careful of us spec-fiction readers. If it is in a speculative fiction genre, we tend to take things LITERALLY. Recent example - Rick Norwood has a story (hope you don't mind, Rick) in fragments and feedback for short stories right now that has a line where the dog flies up the stairs. More than one poster replied indicating they thought the dog LITERALLY flew up the stairs. I suspect Rick was using the term figuratively. So watch out for us!