One piece units are quite difficult to maneuver into an existing house without damage or heartache. They normally are used in new construction and put in before all the walls are up. But, if you can get it in, more power to you! Keep in mind that the tub will need not only a drain, but it must be vented properly. That may or may not be in the wall and under the slab so you may need to crack more concrete and make provisions for that as well. It's unusual that a shower would have a 4" drain line, and it may have been cobbled to gether incorrectly - a shower is normally a 2" drain unless it is quite old, then might have been a 1.5" one (today's code requires a 2" drain on a shower). Some codes require any pipe underneath a slab to be at least 2". A tub could use a 1.5" line, but 2" underneath the slab is better.
So, I see some concrete work in your future. It's hard to tell what you have and its condition from above.
Can't help on the brand/model thing, but hopefully others can.