When should I begin playing bullet/blitz?

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Just rapid for beginner

The speed chess won't do you much good. Your issues still lie with making mistakes from 1 move blunders such as hanging pieces for the most part. That's what you need to focus on, and that generally involves spending time to look at the board for captures, as well as checks. 

check out the section titled "Play Longer Time Controls" at the bottom of this article...

Improving Your Chess - Resources for Beginners and Beyond...

https://www.chess.com/blog/RussBell/improving-your-chess-resources-for-beginners-and-beyond

I am more of an optimist. I don't really believe in the concept of bad habits. Blitz helps your rapid chess too but maybe just not that much. I think it's always fun to hit new records. If you play multiple different time controls, you have more chances to break a record. And if playing doesn't work, you can try to break your puzzle rating.

Lots of my games are over 99, and I've gotten them quite consistently. If you look at my profile, you can see that some of my most recent are over 99. If you look closely at the games, they are very short and easy to calculate the positions. CAPS is not a measurement to tell if someone is cheating.

Hikaru Nakamura doesn't hit above 90% consistency because his players are much better than the average players we play. Don't accuse of cheating until you thoroughly look through the games and you are sure of some foul play

To answer you question though, it really depends on what you feel what is right for you. Generally if you want to improve your chess rapid and tactics are best, but it's always good to sneak in a blitz game or few. Just keep a balance and don't let the fire of chess burn out

When you get stuck, in chess or anything in life, a good general rule is you have to do something different. Don't keep doing the same things.

As for chess, especially when you're not aiming to be a pro, it's important to keep it fun. So yes, play blitz! It's just cautioned against for the same reason people are often cautioned against studying openings... a lot of players take it to the extreme. If you only play blitz then you (more or less) wont improve at all. But if you play blitz and study and analyze, you can improve. If you play blitz and other time controls, then you're doing what most talented young titled players and other fast improvers do (immersing yourself in all aspects of the game) 

Short games (~20 moves or less) from an experienced player can hit 99. Even 1200 vs 1200 can do that if they play some theory followed by a single tactic and someone resigns.

Ideally you look at games that last over 40 moves... but also if you think someone is cheating just report them. The only time chess.com consistently struggles to get rid of a cheater is when they don't have many games, but this guy has over 2000.

If you play a bullet or blitz game you are just spamming moves and showing what you know about the game already, it won't really make you improve. If you stick with rapid you will improve more, you will value the games you play more and will be more inclined to look at them and study them.

If you crave faster games, go to 10|0 or so. Blitz ratings at the lower levels are really tough and it might just discourage you.

Blitz can be fun though, try it out sometime but just remember to play some rapid and study those games for long-term improvement. 

If you are no longer pushing wood, and are actually thinking and planning, then blitz is not terrible. Blitz is a good way of practicing your opening theory and trying out some mid game ideas. 

You can get 5 ~ 6 times as many games in a 3/2 time control as you do in a 15/10 time control. That's 5 times the opening theory you can put into practice! 

I wouldn't expect to get much stronger playing blitz, though. It's more something to do when you want to play chess, but you don't want to think too hard about it. The idea is just to play strong looking moves, and it can help you identify what was strong and what turned out not to be so strong. 

Thanks for the advice, everyone. I really appreciate the feedback. You guys are awesome. 

Depends. If you're flagging every game or getting under time pressure it might help to play some blitz/bullet but if it's just from common beginner mistakes I would just keep on playing rapid/daily.

Were the moves fairly clear/book? I've had some high accuracy games come because of very low risk games where little was at stake and the moves were really without serious danger, neither player ever in any actual trouble for most of the game. So there was little room for blunders that weren't blatantly obvious.