A:AnswerYes, you can use the Sigma 70-200mm with the Nikon d3400. Be sure that you by the Sigma Nikon mount lens, as they make the same lens for the canon mount.
A:AnswerThe DX notation on these lenses indicates that the lens will have an image circle that is the size of an APS-C sized sensor. They can still be used on an FX camera, but you will get a cropped view from the optical viewfinder. They are not full frame lenses.
A:AnswerYes, and both have a minimum focus of about a foot. They are very light weight compared to a kit zoom. I use them on my D7100, my D7000 and D200.
A:AnswerThe NIKKOR 35mm f/1.8G is 100% compatible with the D7000. Nikon DSLR's have used the same f-mount for 50 years. The lenses will all fit. This one happens to both fit and provide 100% functionality - including AF.