Can I use Quantaray AF 28-90mm f/3.5-5.6 in a NIKON D5100? Thanks.

Not easy to understand what you mean with blurred. Could be out of focus or a blurred because of a low shutter speed, shot with the camera in hand. Try switching the camera to Automatic and switch the AF / MF to AF. On the lens the switch that says A M or M/A A, should be in the A setting.

Quantaray makes lenses with a variety of lens mounts. If the lens has a Nikon mount then it will work with the D5100. If it has some other mount then it will not.

No Nikon lens ever zooms automatically, so I assume you mean focus.
The D5100 lacks an autofocus motor, requiring the lens to have one. The older 70-300mm lenses lack this motor, expecting the camera body to have one.
The D5100 will only autofocus with lenses designated AF-S or AF-I. It will not autofocus with older AF-D and AF-G lenses.

No. This lens lacks an autofocus motor, relying on the camera to have one. The D5100 lacks an autofocus motor, relying on the lens to have one. Adding a battery grip does not change this situation.

The D5100 only autofocuses with lenses having an internal autofocus motor. Nikon designates such lenses AF-S, Sigma calls it HSM. Lenses without the motor will only autofocus with the larger and heavier Nikon cameras such as the D7000.

Quantaray lenses are available with a variety of mounts. Assuming you get one with a Nikon mount, then yes, it will work with a Nikon camera. However, unless the lens has a focusing motor, it will not autofocus on the D3000. Some Quantaray lenses have such a motor, some do not.

Those lenses will fit on every Nikon digital SLR. However, the autofocus will only work on cameras with an autofocus motor, the the AF will not work on the D40, D40x, D60, D3000, D3100, D5000, and D5100. Note that this is just the focusing: if you're willing to focus manually then those lenses will work perfectly well on those cameras.

Due to the smaller image sensor of most digital cameras, the lenses will act as if they were about 1.5 times longer. Thus a 50mm lens on a digital camera will give about the same field of view as a 75mm lens would on a film camera. This applies to all Nikon dSLRs except for the D3 family and the D700, which behave in this respect like a 35mm film camera.

You have to decide what's affordable for you, balancing such factors as weight, ease-of-use, and of course cost.

You can see the current Nikon lineup at
http://www.nikonusa.com/Nikon-Products/Digital-SLR-Cameras/index.page

Yes, assuming we're discussing SLR cameras. It can also be used with most Nikon film SLRs.

The Nikon D40 requires the use of AF-S/AF-I lenses. Here is a chart of lens compatibility for Nikon SLRs:

Nikonian.org

If it's a Nikon, mount then yes, it should be fine.

Yes, the Quantaray Autofocus lens will focus automatically on the D80.