What about zdes'? Would that be acceptable instead of tut in this instance?
Not strictly true. "Тут" can be unsuitable for some more formal contexts. But for this course they are interchangeable.
Because "сюда" implies that the action is taken towards here or in this direction. For example, you can look сюда or go сюда. Oh, you can actually use "сюда" here if you use "сесть" (or better yet "садиться" if it's in negative) instead of "сидеть".
I meant in this sentence: "я не хочу сюда сесть" and "я не хочу сюда садиться"
Is the difference between "Я не хочу тут сидеть" and "Я не хочу садиться/сесть сюда" akin to "I don't want to sit [as in, to be sitting for a period of time] here" and "I don't want to sit [as in to sit down] here", respectively? Also, is there a perfective form of сидеть? Is сесть the perfective form of садиться? That's what I recall learning in Russian class many years ago, but now I'm questioning that memory because if that is the case, why would the imperfective be reflexive when the perfective is not reflexive?
What about the word сесть? I remember seeing that word earlier in this course. Are they different forms of the word? If so, what's the difference?
Я хочу сесть (perfect tense) = "I want to have sat" and "я хочу сидеть" = I want to sit