2 - the first - she may not be American
3 - either; the second isn't necessarily continuous, but it is repeated
4 - the second; or "I'm leaving on Friday"; sometimes, colloquially, "I'm leaving Friday". Certainly not 'on this'. There are contexts that would permit 'on that', but that wouldn't refer to the Friday of the present week:
"I don't know, either the week starting on the 4th or the 11th".
"Well, whichever week it is, I'm leaving on that Friday."
This would be rare - probably best not to worry about it.
ps - Afterthought:
If you were pointing to a calendar, you could say "I'm leaving on this Friday", but that context is so rare that even I would ignore it