Yeah, it can feel pretty slow in the beginning, but you get used to it. I think if you were to get everything right and do all of your reviews perfectly on time, the fastest you would be able to level up is no less than once a week. I started just about 27 weeks ago and right now I am at level 25 and from what I can tell that is faster than most people go, so level 2 at 3 weeks is pretty normal.
As for the amount of lessons you should do in a day, it is up to you. When I started out I would do all of the available lessons as soon as I had unlocked them. However, as you go on you will start to have more reviews for each lesson. When I leveled up, I found it comfortable to finish all of the previous lesson’s vocab and then do all of the newest radicals and a few of the new kanji and then save the rest of the kanji and vocab for next couple of days. When you get the radicals to guru, you unlock more kanji, and what I like to do is just do the lessons for the new kanji and leave the vocab for later like before. If you do all of your reviews and then do your lessons like this, you are able to spread the lessons out, but still end up leveling up at a good pace.
There isn’t really anything you can do about the impact of spelling mistakes, besides getting better at spelling . If it’s the english that you are mispelling, I would suggest maybe just double checking your spelling before you hit enter. It’s usually pretty lenient about accepting slightly off english speeling as the correct answer anyway. If you’re struggling with the japanese spelling, I would suggest going over the mnemonics again and saying the kanji/vocab out loud to yourself a couple of times to really cement it in your brain. And just to be clear, there is nothing wrong with getting the spellings wrong or misremembering the radical/kanji/vocab. It’s an important part of the wanikani/srs process. Sometimes you might end up with an item that you keep getting wrong over and over again. People usually call these “leeches”, and everyone has their own way of dealing with them. I usually take a moment to really think about and internalize the mnemonic. Sometimes it’s helpful to try and come up with a new, different mnemonic for the item. jisho.org can also be helpful for vocab leeches because it usually has more definitions and a ton of example sentences to look at.
I wish you good luck in your japanese learning endeavors. 頑張て！(don’t give up!)