Plumbing – this this square hole in bathroom rough in used for

1. Just cut out the T and then drain/vent there.
2. You don't. It should have been somewhere else in the basement. Not sure what they were thinking putting it next to a shower. You would put a backwater valve in a laundry or storage room.
3. Who knows but it sure doesn't look like it's vented.

I cannot think of a logical design for your bathroom. The plumber who did your rough-in must have been high. You have a sink on the left then toilet... then in the corner is what? I guess you could put shelving there but I never design something to hold items to get pee spray. Also if the shower runs with wall it might stick out further than toilet. There is no good solution there.

My advice is to jackhammer up the backwater valve and move that into what will be unfinished space. While you have that ground broken up by shower, make sure it vents. Design your bathroom so that door is on the far left. You walk in and have the sink to your immediate left (might actually be able to keep the T in place). Then toilet after sink. Across from toilet is the shower - you are moving the valve so shower will be installed perpendicular to wall. To vent your shower go straight to the wall and then follow the wall over to sink vent.

If your backwater valve comes in on that wall then basically your costs are concrete and extra pipe. If it comes in somewhere else you might be able to just cut out pipe and reinstall head. You do not want this anywhere near a newly renovated bathroom.

I think you don't "have to" break up the concrete.

1. Let's say your shower/tub extends out 30inches. Whether you have to break up concrete around shower pan or for tub depends on what you install. The last few pans I installed in basements met above grade -slightly. Also note that you will have to find a pan/tub that fits those exact dimensions or you will have to move it or make your own pan. Breaking concrete and moving the PVC over a few inches is a very DIY job.

2. Based on the 30 inches above you would have 15.5" to shower from toilet and per your picture 14.5" on the other side. You would have to check with your local inspector but this would pass where I live. It will be kind of tight but not terrible. Toilets are about 15 inches wide so you are going out 7.5 inches on each side. So you have about 6-7" on each side - most towns require 6" by me. When you add in your drywall you are getting very close but still within most regulations.

3. You put up privacy wall that extend past vertical pipe. I would frame this wall with 2x6 so plumbing access is easier. Pop a vanity on opposite side of toilet and you are all set.

This had to be the configuration that was previously given to your town if the work was permitted. I suggest you ask them for any paperwork associated with it. I know I have to give detailed sketches before any rough-ins so as long as they did things the right way there is probably a sketch of your bathroom.

My opinion... Toilet space is kind of tight but not horrible. I have seen toilets 1 inch from walls. You still crap in them. This isn't as bad. I like the layout though. One person can take a crap without being in the other person's face. Note that having this privacy wall will trap moisture so you better have a good vent fan by the shower/toilet. I like it. If you are tight on space I would try to work with this. If you can add space then I might think about moving the vertical stack over a few inches - really an hour or two of work at most.