Color of the eaves is up to you. I've seen houses with one color on
everything, and other houses - usually in historic districts - with
pretty elaborate paint jobs. Just go with what looks better. If you
have a separate trim color, normally the eave will go the wall color.

Flat paint is fine. In fact, if I see one house a year with semi-gloss
on the siding or eaves, it's a lot. And I can't remember the last time
I used semi-gloss on the exterior. It's been years and years since I
did that, except for doors and occasionally windows.