This isn’t intended to be snarky, but to answer your question directly: what’s happening is that it’s taking you a long time to get 90% of the kanji on level five to SRS stage 5 (Guru-1).
No, not in my opinion. In my opinion you need more reviews and possibly even fewer lessons. More below.
The only study habit that matters on WK is doing your reviews every day. Real life happens, and we all miss a day here and there, or don’t finish all our outstanding reviews sometimes, but the more often this happens, the harder it gets and the slower you will go.
Those accuracy levels sound fine to me. Your problem is very likely that it’s mostly the same 10%-20% of kanji that you answer incorrectly, and they are preventing you from leveling up.
There really is is little rhyme or reason to readings (though you will start to notice some patterns as you progress). It’s normal to find readings harder in the beginning. Rote memorization is truly the only way.
Leveling-up is gated by guruing kanji, not by vocabulary, but vocabulary helps to cement the meaning of characters. You’ll eventually start to notice patterns with the various readings, too.
There are a few reasons readings are harder. For one, every character has multiple unrelated readings. For another, vocabulary almost always reinforces the meanings (当て字 are the exception) but different vocabulary readings make remembering the correct kanji reading harder.
Finally, remember that vocabulary is the entire point. Learning the meaning and one reading of a couple thousand individual kanji is little more than a party trick. Learning to read vocabulary words using those underlying characters is a life-changing skill. The more vocabulary reading you do (eventually outside of WK as well as inside) the better you will learn the individual characters.
Advice
Keep an eye on the “progress” section of the dashboard (here’s mine at the moment):
As you’ve probably realized, you need to get all four blocks to turn green on 90% of those characters before you’ll level up.
Since you’ve just started level six, you’re probably still doing vocab from the prior levels but you might have started seeing level six kanji. What usually happens is that most of them progress at the same speed (the green bars move to the right at the same speed) but you keep getting the same few wrong day after day. If after a week or two, most of the items are fully green, but a stubborn few still have just one or two blocks green then those are the ones you need to focus on.
It’s counter-intuitive, but doing more, out-of-band reviews (with extra-study or the self-study script) can make a world of difference.
If you end up in this situation where a handful of characters are preventing you from leveling up, I’d strongly recommend taking an hour or so one day and do multiple iterations of “extra study” for recent lessons (or even better, use the “self-study” script).
Extra study won’t let you finish the session until you’ve answered all the questions correctly. Once you finish, though, go back and start over again from the beginning. You’ll almost certainly find it easier the second time. Continue iterating like this until you’re 100% confident in every answer.
[The self-study script let’s you re-quiz just the items you missed in the prior iteration, so this process can go faster with the script since you don’t have to keep re-quizzing the items you already “know”.]
If you spend the time doing this even once, I think you’ll be amazed at how much easier the reviews go on subsequent days, and how much more quickly you level up.
Before the extra study feature arrived, I’d just glance at the “progress” section before starting my reviews, and quiz myself on the meaning/reading items for any items that haven’t turned completely green yet. I’d click on them to get the right answer if I couldn’t remember. Again, I’d wait until I was 100% confident I knew them all before starting my formal reviews (and then inevitably miss a couple anyway).
Final point: repeated, “extra” reviews of Apprentice items (stages 1-4) is NOT CHEATING. You cannot have too many reviews of early stage items. The more iterations you can get in, the better you will remember them.
Formal reviews of later stage items (guru - enlightened) are better thought of as “retention tests”. You need to prove you can still answer them correctly after not seeing them for weeks or months. Apprentice items, though, benefit from as many review iterations as possible.
Finally, as other have pointed out: ultimately speed doesn’t matter. It’s far, FAR more important to learn to read comfortably and easily than it is to get to level 60, no matter how long it takes.
Have fun.
Oh: regarding doing more lessons/day.
I don’t think doing more lessons will make you go faster. Lessons are like getting into college. Once you’re in, you need to answer items correctly four times in a row to graduate (or make it into the next year).
It doesn’t sound like your gated on an insufficient number of Apprentice items. Instead, it sounds like you’ve got kanji that gets stuck in Apprentice, preventing you from leveling up. Focus on them, not on adding more.