#1
When I try to play simple arpeggios (like in Wake me up when September ends or Behind Blue Eyes or anything of that nature, I am terrible at it. I feel like I have no control. I don't know if its my picking pattern, the way I move my hand/wrist, but inevitably, it never feels right when I play it and I usually mess it up/play the wrong note. I will often play it too fast or too slow. Are there any exercises I can practice, videos on technique, or anything else I can do?
#2
Use a metronome. Play it slowly, build up speed until it is clean and correct.
Almost all skills feel unnatural when you're not good at them!

Maybe try simple open/ barre chords and arpegio them on all 6 strings back and forth with a metronome build up speed slowly and ONLY step it up a notch (maybe 2 or 4bpm more when you're starting to struggle) when you're 100% accurate when you play at the tempo. Skipping that will be wasting time with something you can't play.

I can't comment on your technique because that's something you might want a guitar teacher or friend who knows how to play to comment on.

But for now, in the future whenever you feel like you're not being accurate in any other technique bust out the metronome. It's the answer for almost every accuracy-related problem.

There's quite a few free ones on the web.
There's a good chance that what I've written above is useless and if you take any of the advice it's your own fault.