I am replacing a standard 5 foot tub on a cement slab. I have read conflicting instructions in regards to when to install the drain. I have access to the back of the tub through a panel in the wall. Do I install the drain before or after I place the tub in its location? Also the new drain is PVC and the trap is copper, can I easily connect these, or is it best to use a copper drain? The old drain has a short copper pipe (tailpeice?) that screwed onto the 'T' section of the drain and was connected to the trap. I plan to reuse or replace this section. And lastly, when I removed the old tub, the old drain surprisingly pulled right out of the trap. Shouldn't this have been secured in with sodder or is it OK for it to simply sit into the trap? Once I connect the PVC drain to the tailpeice, do I need to sodder in the tailpeice to the trap? Thanks in advance!

You're going to have to be more specific and we're going to have to come together on terms before I can even understand your problem. First the terms.
pop-up tub waste and over flow = a lever on a face plate that mounts on the front of the tub under the spout and also has a pipe in back that extends down to a tee that seats the stopper.
Tub shoe= The drain itself that fastens to the bottom of the tub and connects to the branch, (middle part) of the tee on the waste and overflow.
Tailpiece= the pipe that extends out the botton of the tee and connects in to the trap.

The tub is set first and the rest connected after it's set. If you've never set a tub before there are adjustments, both to the pop-up stopper and the tub shoe connection, that I can't explain without being there.
As for the trap, Look and see if there isn't a compression fitting on top. The tailpiece didn't just "sit" in the trap or you would have had water all over. And you can't solder PVC to copper. Setting and connecting up a tub is major surgery and I would do all the "scutt" work and purchase all the materials and then call in outside help to complete the job. Happy New Year, Tom