Is it normal to go weeks without talking to friends?

I'm guilty. :(

I feel burnt out from my school work sometimes. Before uni, I was so on top of my correspondence; now, I'm an asshole.

You could try to force yourself to make contact with them on a regular basis (once a week, at least), just to maintain it. Even if it's just something small.

Mmm, this one is tough. I would be careful with this because friends might take this in a way that makes it seem like you don't like talking to them anymore. I know people might go "friends should realize people might be busy" but I believe friendship too takes work and effort from both sides to keep alive also, mostly for friends that you normally talk to an insane amount normally. If it is just that you're busy, let them know so they won't get offended if you can't contact them. If you just get tired of initiating conversation, its fine to back off and let friends try sometimes instead. But don't just go weeks or months without talking at all, it'll kill some friendships. Yes "some", some can do that, some can't.

I know this because some of my most important friends I've made suddenly gave this "I'm too busy to be bothered with you" vibe by both not responding and/or when they do, its short uninterested responses. Not just once or twice but for several weeks. At that point, things can fade kinda quick.

I think that's normal if you are
a) best friends forever
b) not that friendly

I have already gone for weeks and months without talking with a best friend of mine (partly because he lives in London, but that's no excuse, that's what internet is for), and when we finally met again we talked and laughed and had fun like if these were just a few days.

sorry honey, he sounds like he's moved on, and so should you.

Another childish rant by someone not old enough to legally drink, guess what people most "friendships" don't last very long much less yrs and yrs. Most people that are "friends" really just hang out because its mutually beneficial. You kids are in for a real rude awakening when you hit the real world.

Sweetie, when I was in my school years (Just a few years ago), I didn't talk to anybody. I only had a few good friends, and I rarely spoke to them. If I could go my whole childhood without talking to my friends, anyone can go as long as they like.
But really, I barely spoke until I was 17. And that was only when I was picked by a teacher. Other than that, nod and shake.

I don't have any friends.

It's normal to not feel the need to talk to your friends. If they're truly friends, they won't mind.

In your case, it sounds like you actually want to talk to your friend. If so, then no, that's not normal. If you want to talk to a person then you should talk to them. Why give someone the silent treatment for no reason? (if that is the case)