1) I don't want to reinvent the wheel like I've kind of had to do with my main project, I'm almost just interested in some rapid prototyping to get a couple ideas out while the creative urge is still in me. What's a good engine, framework, or tool you would suggest to forgo a lot of tedium associated with writing a game from scratch in HTML5?
I would usually highly recommend ImpactJS, but this is not free. There are free engines like CraftyJS which seem to get good feedback. You can find a list here: https://github.com/bebraw/jswiki/wiki/Game-Engines
2) Once I've managed to make something, is there any online community that allows HTML5 game submissions, kind of like Newgrounds and Kongregate for Flash games? Or would I most likely have to invest in some cheap hosting to get them out there?
You can host for free on GitHub, but there are also plenty of other communities where you can host your game. Look into Chrome Web Store, for example. With a bit of googling around it shouldn't be difficult to find one you'd like to host with as they are quite common.
3) Any other advice you may have to pass on after experimenting with HTML5 yourself.
- Browser compatibility is a pain in the butt. Test early (as I'm only working on HTML5 games for fun in my spare time I'm kind of half-assed about this and only really focus on Chrome and Firefox)
- I recommend Chrome Canary to use as a primary browser during development.
- Chrome Dev Tools are extremely useful