Yes the SB-700 can be used remotely, however, the on board flash has to be used to control it thus technically you cant turn it off as it still has to send a signal to the flash unit. You can set it in the menu to -- but the flash will fire though you may get some residual light from the flash, you could of course buy the SG-3ir which sits on the hot shoe and so stops the residual flash from affecting your images.

I dun think so. I have never tried the D5100 but if it doesn't have a Built-in Camera flash commander option, I guess it doesn't.

http://support.nikonusa.com/app/answers/detail/a_id/9520/~/nikon-creative-lighting-system-%28cls%29

http://support.nikonusa.com/app/answers/detail/a_id/11938/~/how-to-use-the-built-in-speedlight-in-commander-mode-to-control-remote This one might not be updated yet.

Or if you have 2 SB700, you can attach one to your camera hotshoe to act as a commander unit for the other off-camera SB700.

But still check with your local Nikon representative first.