Yes, but it is a DX-format lens. On full-frame (FX) cameras, it will automatically trigger 'DX Crop Mode,' resulting in a lower resolution image to avoid vignetting.
With a maximum aperture of f/4-5.6, it is best suited for daylight or well-lit environments. However, the built-in VR helps stabilize shots in slightly dimmer conditions.
Yes, it features an AF-S Silent Wave Motor, meaning it will autofocus on all Nikon DX DSLRs, including entry-level models like the D3000 and D5000 series.