Are my lenses from my Nikon D3000 compatible with a D7000?

I'm a freshman photography student and want to upgrade my current camera to a D7000. My current D3000 came with a AF-S DX NIKKOR 18-55mm f/3.5-5.6G VR lens. I also have a AF-S DX Zoom-Nikkor 55-200mm f/4-5.6G ED and a AF-S DX NIKKOR 35mm f/1.8G. Will these lenses be compatible with a D7000?

I also experience some vignetting with my prime lens, objects near the corners sometimes appear warped or really soft (compared to the rest of the frame) when I'm shooting with a wide aperture. The corners even sometimes appear blurry. Will this still happen with a D7000?

They'll work perfectly - it's not good to shoot wide open with ANY lens, so your vignetting problem with the 35mm will probably persist.

The D7000 has a body motor, so it can use a wider choice of lenses than the D3000, but you shouldn't have a problem with your existing lenses.

Yes, the lenses should be compatible with the D7000. As a rule, Nikon cameras with DX sensors (e.g. D3100, D5200, D7000, D7100) are compatible with all new AF Nikon lenses, such as your lenses. I think the vignetting problem you are having is caused by the lenses, though the sensor may have a little to do with it. Therefore, yes the problem will persist on a D7000.By the way, the D7000 was just replaced by a newer model, the D7100 today (3/14/13). If you are looking to invest in a good camera that you won't replace for the next ten years, I would recommend getting the D7100 instead of the D7000.

All lenses which work on your D3000 will work on a D7000 or D7100 (the replacement for the D7000).

Vignetting is darkening of the image at the corners. What you describe is not vignetting, but distortion (warped image) and sharpness (softness).

The results you have with your current camera will be exactly the same on a D7000.

All Nikon AF or AF-S lenses are fully compatible with the D7000. The AF lenses that wouldn't auto focus on your D3000 will auto focus on the D7000 because it has a focusing motor in the camera body.