Maybe. This lens will allow you to shoot in lower light conditions than the 18-55mm lens that came with your D3100. This might include shooting indoors without flash and in museums and at shows with fast moving people, assuming you can get close enough. I own one and like it but I also have other more general purpose lenses.

I have a feeling that if you have to ask, this lens might not be the right choice for you. A wideangle lens that goes from about 10-20mm will open up a whole new world of photography not available to you now (good for some travel shots, but stitching photos together might also work) and a lens with more reach such as 18-105mm or 18-200mm might have a more immediate benefit. Portrait photos typically use a lens somewhat longer than 55 mm (maybe 85mm on your camera). One thing that is especially nice about the 35 mm lens is its compactness. With this lens I can put my whole camera into a vestpocket pouch and shoot images in an art museum that does not allow flash. I have framed copies of several masterpieces I've taken this way.

Because many people like a little more reach, the kit lenses of cameras that cost a little more come with the 18-105 mm lens. Also there is a 55-200 mm lens that can provide extra reach without duplicating what you already have.

yes! D7000 is a camera in DX format and this lense too.

The D40 has no auto focus motor, but any AF-S lens is compatible to the D40 because it has a built in motor.

No. With this lens you need to "zoom with your feet", but the advantages of this sort of lens are it's size, weight, sharpness and and the ability of it's wide maximum aperture to gather light. It's ideal for general photography, street shooting, and low light photography without flash.

That will work perfectly as the 35mm lens has its own focusing motor. The sb-400, especially when bounced, will give plenty of wide light to capture with the viewing angle of the 35mm lens! Cheers!