Laundry tub draining into basement floor drain - open pipe into drain hole

We've recently seen some water in the (finished) basement of our (100+ year old) home when we run the washing machine or use the basement shower. This has led to some investigation and some horrifying discoveries.

Basically, it's like this:

1) The laundry tub (into which the washing machine drains) and the basement shower drain into the same PVC pipe (t-joined). The shower drain is in the WALL in the CORNER of the shower and will get backflow from the laundry tub sometimes. The shower is tiled (badly, seeps water) and recent construction in the neighborhood (they redid the sewage and water mains over the last 2 years) has probably not helped. I know how horrible that is, but that's not the main problem.

2) Said PVC pipe then runs out along a channel in the floor to what I can only assume is/was the floor drain for the basement. The pipe terminates in a 90-degree elbow connector, and a stub of pipe extends into the floor drain hole.

3) The water we've seen in the basement is caused by the floor drain backing up, basically... I got in there today to see what was going on and found standing water in the drain hole.

Now I'm no plumber, but this seems disastrously wrong to me. So my question is this:

Is it DANGEROUS? Right now, my goal is to at least reestablish equilibrium with this hack job so that we have a shot at using the laundry without flooding the basement. I can live without the shower (and plan to simply cut and cap the end of the pipe that leads to the shower drain).

Right now I've put some Liquid Plumr into the drain to try and unclog it. Phase 2 probably means going to the Roto-Rooter man or something similar.

It seems obvious to me that the long term solution is to gut the basement and try again from bare floors/walls. But that's out of reach at the moment.

Any and all suggestions are welcomed.

Scott

Phase 1 was a waste of time and money.

I would go to Phase 2 but avoid companies with rooter in their name as premium pricing is associated with the name rooter.

A floor drain should have a trap in it. A trap SHOULD have standing water in it - that is what traps the sewer gasses from getting into the house. But, both the laundry sink and the shower should have their own traps (and vents) and connect to the sewer directly, not drain into a floor drain. None of the add-ons (the laundry or shower) would pass code, and probably (I hope) were never permitted and inspected. They both should be redone. how best to accomplish that would depend on the layout of things.

One more thing. Do not use chemical drain cleaners. They not only don't work, they can damage you plumbing, and create a hazard for the plumber who eventually will have to work on the problem.