I've been looking at my analytics lately and I've been a little bit skeptical about them. It seems like a decent amount of people have visited and downloaded my game, but then I remember how many times I've seen and downloaded my game and now I'm wondering if downloading and visiting my own game makes the analytics think that someone else is visiting downloading my game and skewering my analytics.

I don't think so. It shouldn't. Your game is probably more popular than you thought.

It depends on whether you're logged in or not. If you download your game while logged into Itch.io, it won't trigger a download or page view.

If you go to a different browser where you're not logged in and download it from there, it shows as a download.