Will a CPC PHASE 2 CONTINUOUS lens work on a nikon d5100

When you connect a lens from another firm, or an old one without a chip, The camera can't work in the automatic settings. So not one scene and also you can't use the A, S, P and Auto. Really only manual is possible. And you have to dial in everything. like shutter time and you have to set focus and Aperture on the lens.

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.

Sirius makes lenses with a variety of lens mounts. If the lens has a Nikon mount then it will fit on your D5100. However it will not autofocus, nor will the camera be able to set the exposure. In fact the exposure meter won't work at all, and you'll have to shoot in the Manual mode (turn the mode dial to M).

There is no way to really answer this question as the camera was dropped. If it was dropped with the lens, then the problem could be either in the body or the lens (or both). If you have another lens try it and see if you get the same result. Otherwise you are probably going to have to take it to the shop or send it to Nikon

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.

In either mode, you're zooming by turning the zoom ring on the lens? In live view mode, if you zoom in by pressing the magnifying glass button, all you're doing is zooming the display, not the image itself.

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.

This is not a solution but the same kind of problem.

I just bought a Nikon D5100 and found that my Sigma 105mm macro has a problem. The camera will not power up, but if I turn it on, untwist the lens and then twist it back in, the camera powers up. If I leave it for a few seconds, it powers down again. Provided I keep taking photos, it works, but this is not acceptable because it can take several seconds to get a focus on a close-up, and by time I get the focus, the camera powers down again.

I never had any problems with this lens on my Nikon D80. I also use several lenses, all of which work well with both cameras. It's only the Sigma that has the problem. And I did clean the contacts with a proper contact cleaning solution and a swab, but still no joy. My lenses are made by Tamron, Pro Optic, Nikon and Sigma, and the only problem lens is the Sigma.

Quantaray makes lenses with a variety of mounts for a variety of cameras. A lens with a Sony mount, for example, will not fit onto a Nikon camera. Assuming the lens has a Nikon mount, it will fit on the D5100. However, the D5100 requires the lens to have an autofocus motor. If the lens does not have such a motor then it will not autofocus. It will still work fine as a manual focus lens.

The Canon lenses are FD mount which means that you will need to get an adaptor to convert the FD mount to fit the F mount on the Nikon. An example of the mount can be seen here:

http://www.rugift.com/photocameras/canon-fd-nikon-adapter.htm

As for the speedlights the hotshoe mount will accept them on your Nikon, put them on with fresh batteries and try them out.