Do I need a certain type of trap to do this.
only if they are seperately vented and each protected by its own trap, this is very general for more detailed info contact a plumber in your area
Both should already have a trap, you can add another if you like. You may need to ask a professional if there is a consturction code involved in this sort of renovation.
Yes, you should be able to run both the wash basin and the tub/shower drains thru the same pipe. If it's PVC instead of the old galvanized, or rigid copper, you can just cut it with a hacksaw and get a rubber (called a Fernco fitting in most parts of the country), and clamp the pipes into one another with a screwdriver. It requires a little planning so if you're not quite familiar with plumbing you may want to ask for help. The tub/shower line should probably have the trap located beneath the floor, while the trap for the wash basin would be located under in the vanity, under the sink top.l
