Tailpipe of sink not aligning with P trap
It looks like you have 1.5" pipe there, and, for some odd reason, someone decided to convert it to 1.25" right off the sink drainpipe (and with glued PVC to boot). This makes for some frustrating work, especially, if that drain ever gets clogged (good luck getting into that P-trap).

I would make the same cut Michael Karas made on the pipe coming out of the wall, but I would downsize to 1.25 at that point and install a standard 1.25" hand-screw trap. You can glue this convertor on and then buy a PVC P-trap kit (you will likely need an extension pipe cut to size to make the trap reach the existing drain). 



The new tail piece screws into the adapter and can be moved back and forth as needed to ensure you line up with the new drain. And all your connections are hand fittings now, so drain maintenance is far easier.