If you're looking for a compact camera then I would suggest a lower-end or used GoPro. Unfortunately that's my only experience with timelapse cameras outside of using my DSLR. One thing I do like about using my GoPro for timelapse is I put it on an "egg timer tripod". So the camera slowly rotates as it does the time lapse. Adds a neat little effect.
Yep, something like that. I have a Vello Shutterboss but there's 3 or 4 different incarnations of the same thing with different names and prices to go with it.
With that said, go to the bottom of the shooting menu on one of those D7000's listed in your profile. There's an option that says Interval timer shooting that might be of interest to you.