Build Shower Platform & Install Above Ground P-Trap in Basement Shower

Hello,

I'm new to this site. I tried to find the answer in previous posts and did find some great info, but I still have some questions

This is what I want to do:
Install a corner shower with dimensions 36" in x 36" in the basement, build a platform, & add an above ground p-trap.

SOME DETAILS ABOUT BATHROOM:
--House Built in the 50's
--Small basement bathroom 6ft x 9ft with corner shower
--2 inch Copper drain coming up through concrete slab
--Drain sits 1/2 inch below floor level
--Concrete is dug out around copper pipe about 2 inches on either side
--Drain has no threads and has some corrosion

Kind of looks like this except pipe NOT flush with floor:

FLOOR LEVEL (`= symbol)

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THE MAIN PROBLEMS IN MY OPINION:

-- NO p-trap (drain connects to main drain via washing machine drain-I am fairly sure of this because soap suds occasionally come up during rinse cycle, it's 6 feet from it, and, I checked to see if there was any standing water by sticking a wood stick and piece of cloth down there-both were dry)
--we have a root problem and had a Roto Router cut the roots away once. When we found out about this problem was the day the much of the basement flooded. This worked for 8 months with only suds coming up drain from shower. A week ago, after having 20 people over for Thanksgiving the water from the laundry has caused much more water to come up through shower drain.
--The pipe coming out of the drain is a a bit corroded, somewhat rough, and sits below floor level.
--I would like to avoid digging up the concrete and replacing the pipe.

WHAT I'm THINKING ABOUT DOING:

Building an 8in wood platform and installing p-trap in that space, and creating new drain w/ PVC for the shower.

WHAT I'm NOT SURE about:
Can I salvage the current drain?
How do I create a waterproof seal between the new PVC and old copper drain?
Will the p-trap solve both the problems of sewer gas & water backing up from laundry?



I tried to make this as clear as possible, please let me know if I left details out Thanks! Josco