I'll give it a shot...
Wide angle built-in: I am not aware of any consumer grade or better worth using that has built-in wide angle. Adding a lens usually means a screw-mount (suggest 0.7x wide. Any wider and you star getting a fish-eye effect).
A mic jack needs to be included on the camcorder. You need to decide if your budget can deal with a good wireless lavaliere or not. Sennheiser G3 is a start - there are others. Base station portability may be a requirement.
Depends on the camcorder. Wort case: buy an optional rechargeable batter from the camcorder manufacturer.
Budget is likely too low (entry-mid level consumer grade), but the Canon HF R series might work.