So how I understood it, the way to learn Japanese is through immersing a lot. As a beginner you would start with Kana, move to a deck with the most common vocab and after that you mine your own sentences, until you become fluent, and then you can start to output, is that right?
Basically yes.
Since it is recommended to learn a sustainable amount of new words a day, does that mean, that I have to sentence mine that amount?
If that is what you have decided to do, yes. But I personally recommend not stressing out about this. Mining the words is not actually how you learn them. It's the exposure through immersion. Mining sentences just artificially increases the frequency of seeing those words through Anki, making you more likely to remember them.
For example, if I want to learn 10 new words/sentences a day, would that mean, that I have to mine 10 sentences that day?
Technically, yes, but like I said above, it's not exactly that serious.
Because If im watching multiple episodes and try to mine all the i+1 sentences, wouldnt the amount be way higher than that?
It could, yes. It depends. You want to focus on quality over quantity when it comes to mining cards. If you only mine 5 cards one day, but they're all high quality, you're winning.
Or does mining mean, that you mine every i+1 sentences you come across, add them to your deck, but you dont learn all of them one that given day, instead you still learn only 10 new words a day?
Generally, yes, this is the most sustainable way to do it. Some people rep all the cards they mine everyday on the same day (for example if they mined 50 cards that day, they would do all 50 cards) but this is only something I support if you're a very experienced anki user and you're at least intermediate in the language (2C+)
The thing about 1T sentences is just because a sentence is 1T doesn't necessarily mean it's a good sentence to mine. There are other factors I like to consider. I can expand on that if you want.
Another question I have is, If I happen to stumble across a word, but there is no sentence to it, should I force myself to search for a sentence containing that word and add it to the deck?
Some people do this, but I personally don't and it's not something I would recommend based on personal experience. A sentence is so much more impactful if it's within the context of content you're enjoying. If you just search a sentence bank for any random sentence, the effectiveness is way lower because you have no personal connection to that sentence. Just skip it.
And how to I approach immersion, in terms of freeflow and stopping every time i dont understand a word. For example, I watch an anime, but I dont try to stop every sentence and I have an anime, where I stop every sentence to understand it 100 percent. Do I sentence mine the one, where im stopping the anime?
You will want to read the roadmap article about intensive and freeflow immersion. Both activities are important and cultivate different skills. Intensive is going to be the most conducive for mining, but that's not to say you can't mine from freeflow immersion either.
When I sentence mine new words, should I immediately try to remember the pitch of that new word?
It's a good practice to do, but it's not something you need to grade/test yourself on as far as passing or failing an anki card is concerned.
And should I only start outputting, after I had plenty of immersion ?
That is what is recommended, yes. The roadmap addresses when would be the best time to output.
and what if i find a sentence, that has two unknown words but i really want to learn both words? Do I search for two sentences with both words being an i+1 or do I continue searching for i+1 and ignore the sentence with the 2 unknown words?
This is personal preference but I always just wait until I get a good 1T sentence for both words separately. Or I just don't bother.