Generally, you don’t. You just learn that, say, 川口 is read as かわぐち while 人口 is じんこう, and you don’t care which one is on’yomi and which is kun’yomi. After a while, you just start to get a feel for which reading goes where - you’ll even be able to intuit the readings of words you’ve never seen before.
As for item one, there’s a script you can find below that, once installed, will allow you to review what you’ve learned. I’ve noticed that there’s a difference of opinion on how helpful reviewing is to the SRS method of learning, but I’ve installed the script myself and have found it beneficial so far. Your mileage may vary.
1.Try reading the short stories in tangoristo, and as others mentioned, the bookclubs. I think absolute beginner is the one for beginning learners
Kunyomi reading are often used when the word is standalone(or with hiragana attached) and onyomi is used when the word is a compound word i.e two words merged together. typically there are exceptions to this as sometimes the kunyomi is used for compound words. like others said you do get a feel for it.
Lingodeer - it makes the experience less monotonous and a bit fun. However I do have genki, and I listen to Curedolly from KawaJapa to supplement. Japanesepod101 is a good resource as well.
I’m not certain about speaking but for listening, you can try to listen to JLPT test preparations. Tangoristo has audio of all the articles that you can listen to as well.
As a side, If you are into anime, I find Shirokuma Cafe to be good for beginners. if you watch it on animelon with japanese subtitles you can practice your listening and reading as well.
There is a link of all the resources both free and paid on the forum .
There’s no need to, really. The reviews are the practice. I’d say any kanji exposure you get from grammar study is probably enough for now.
With enough exposure it just happens. Kun vs On isn’t something I’ve ever had to focus on specifically, and the common readings will fall into place pretty quickly without much effort.
Give Lingodeer a try. It’s an app that, in my opinion, is perfect for learning fundamental N5-N4 level grammar. You’ll need other sources for more advanced grammar, but LD is a great place to start if language apps are the kind of thing you’re into.
No advice here, sadly… My main goal is to be able to read Japanese, so I’m neglecting speaking and listening, at least for now.