Seth is a man. Shouldn't it be jeskun?
Correct that تسكن would be feminine 3rd person, but it is also masculine 2nd person. Here you are talking to Seth directly so you are using the 2nd person.
لا انت لا تسكن في مدينتي يا سيث
It goes both ways in Arabic. As you can write down the subject pronoun or just drop, as it can be understood from the verb's conjugation.
Shouldn't the word after no be "anta"?
the pronoun is not necessary because the verb conjugation already includes it. same with romance languages
That doesn't apply to French, which I think counts as a Romance language.
'Taskun' already means 'you live', while askun means I live.