Two problems; first issue is that the drain from the sink does not line up with the p-trap... what can I use to connect the two? The other issue is that the drain from the sink is much too long... can I cut the drain pipe to make it shorter?

Are these PVC drains and traps or what material. Both the tail piece from the sink and the line into the wall have slip joints so you have those 2 adjustment points. Both can also be cut or lengthened if the slip length is not enough. Installing Kitchen Sink Drain Plumbing With S-Trap and Slip-Joint Fittings (http://www.hammerzone.com/archives/kitchen/sink/stainless/drain.htm)

In addition to Bob's post: Install sink, don't worry about drain. Then use fittings to connect sink drain and wall drain / trap. Sometimes it is better to replace trap as well. It costs few pennies and saves you time. Yes, you can cut off sink drain... Let us know how you did... Milo