I pulled up the tile in my bathroom. Water was underneath and had rotted the wood nearby. Now I have a concrete pan underneath where the tile used to be that slopes toward the drain. Can I put a shower pan over this concrete pan? If so, do I need to extend the shower drain?
At this point you really should do it right. Since this is the basement floor, you will be placing the shower pan on the concrete. You'll want to adjust the drain so that it can connect correctly to the shower drain. If this concrete is already sloped (and it sounds as though it may be) you may be able to remove the sloped part if it was poured on top of the slab. Otherwise you could use some leveling compound to create a flat surface for the shower pan.
I'm assuming now that the rotted wood was in the walls. You should use a product designed to back shower tile such as a cement backer-board rated for this use. Your building materials supplier should be able to get you the right product. Follow the manufacturer's recommendation for proper installation and surface preparation needed before applying the tile.
Be sure to remove and replace all the rotted wood while you have this all exposed. It won't get better on its own.