Yes, the DX II version features an internal autofocus motor, allowing it to autofocus on all Nikon DX DSLR bodies, including the D3000 and D5000 series.
It is designed for DX sensors. While it will mount on FX cameras, it will produce heavy vignetting unless used in DX Crop Mode or at the 16mm focal length.
The lens uses a standard 77mm front filter thread, making it compatible with most professional circular polarizers and ND filters.