Yes, yes/maybe, yes.

To amplify,

Yes, you can run another wireless access point (you don't want to use it as a router) off of this cable. You can use the same network name, and I believe most systems will accept it as the same network; I'm a little dodgy on this one, since the last time I did it was years ago with a couple of Airport Base Stations.

You can definitely put a new end on ethernet cables; all you need is a crimping tool. You can find these at Home Depot, actually.

I am the Doctor, and THIS... is my SPOON!