English doesn't typically have rising intonation on wh-questions. If you pronounced "When do you come?" with a rising intonation, it would be marked as having some special intended interpretation (e.g. "WHEN ...?" with a rising intonation would be a request for a repeat of the answer, and would likely be prefaced with something like "Sorry, I didn't catch that. WHEN ...?"). But as a regular interrogative, there wouldn't be a rise in intonation here for this wh-question.
For yes-no questions, there would be for English, though I'm not sure about for Swedish.
"I usually come to work every morning before six; when do you come?" It works. You potentially change the meaning if you ask "When are you coming?" because then I would think your are trying to find out the time of a single arrival (either the next in a series or a sole event), rather than trying to find out the time of a recurring arrival.
No, but you could say "när kommer ni?" to ask when do y'all come.
du and ni are both subjects. dig and er are objects, so would not be used in this sentence like that. The subjective case (nominative case) is different than the objective case (dative/accusative case). The same thing happens in English to separate "she" from "her" or "I" from "me", we just don't happen to separate English subjective "you" from objective "you"; Swedish does.