AF and AF-S lenses will work on your D7000, as well as D lenses
As for FX on DX body - no reason not to use this combo. I do (well the one FX lens I have), but as your DX sensor will only use the (smaller) centre of the FX lens, you are in fact paying that little extra premium for glass you're not going to use.
On the plus side though, only using the centre of the FX lens means you get that 'sweet spot' and no issues from the edges of your FX lens as the sensor will never see them