Yes.

yes

In dx crop mode.

Yes

The 10-24mm and 14-24mm are not ideal for portrait or nature photography. They are wide lenses so would normally be more used for landscape, though you can get some funky effects with wide angle lenses. For portrait I would much more recommend the 50mm 1.8D or G or the 85mm 1.8D or G. For nature, it depends what kind of nature photography you want to do. I would say probably a 300mm focal distance is probably the minimum that you want. I have shot deer with a 200mm but it isn't ideal and to get a really nice shot you have to get much closer than you would really ideally want to (mostly they just run off, fortunately. If you want to do insect photography, I would would say that the best value lens is the Tamron 90mm 2.8, it is cheap feeling and noisy but optically it is great.

Hope this is useful.

Yes

Yes

yes

Yes

At 10mm it would certainlt be wide enough but you may get a bit of distortion going that wide.

yes

Any DSLR lens when mounted on a DX camera (D7000 among others) will have a crop factor of 1.5, so the 10-24 will have an effective field of view of 15-36