What kind of block wall is that? I've never seen anything like it. It kind of looks like brick, Is that below grade?

It is a poured wall with a brick like pattern used in the forms. Yes. That wall is below grade (in my basement).

That's really neat. Good choice.

The 3" is obviously for the toilet.

The 2" in the corner is for the shower. You could not use the middle 2" for a shower because even if it were a corner drain, the shower would be in the middle of the room and likely would be too close to the toilet (need 15" from centerline).

The 2" in the center is still bizarre, though, because even for a sink it will be oddball. It willhave to go on the left side of a vanity so that you have that 15" clearance, which means the drain will come down and then go left, rather than back (which is customary).

The 4" appears to be a cleanout, but, like the sink drain, seems oddly close to where the sink would go, and will cut off the last 3-4' of the room.

Have you asked the contractor or consulted the plans? Or is this a house you bought after it was otherwise done?

It may be worth your while to break up some of the concrete and move the 4" clean out and the middle 2" pipe to locations that make more sense.

I would say the 2" in the corner is for a tub/shower. It should be trapped. The 3" is for a toilet. The next 2" is for a sink. I am going to guess the 4" is a clean out for the main drain line. It looks like you could install a finish cover plate on it. It would be unusual to see that in a residence but since it is a basement you might not care.
Without having all the dimensions it looks like you might be okay with the placement of the tub and the toilet. The sink connections doesn't seem like it will work. You might be able to sit the end of a vanity over it. Maybe a large enough vanity will cover the clean out as well.

Thanks for the advice. I agree that the 3" is for a toilet. However, neither of the 2" pipes appear to be trapped. What is a good way to tell (besides removing the concrete)? I have poured water down them and neither held any. Further, they are both with in 18" of the main 4" drain out of the house and when water passes through the main line, I can hear it clearly through both of the 2" lines. If one was trapped, I would expect the sound to be muffled. Please advise.

A real plumber can chime in, but wouldn't the sink be trapped above the slab (i.e., in the vanity)? Shower is still a problem.

Thanks heimert. I agree, the sink will be trapped inside the vanity. However, if one of these is for a shower, I would think it would be trapped below the slab.

I think the idea w/ the 2" sink drain in the center of the room is to build a wall to divide the bathroom into 2 separate areas. The wall would conceal the pipe, and the vanity would back up to the new wall. The door to the toilet/ shower room would have to open outward.

The shower would typically be trapped where it connects to the drain. If you can't see any evidence of a trap I would say you don't have one.
It looks like you will need to cut up the concrete and have one installed. It's an inconvenience but not that big of a deal.

This is a circuit vent. The 3 inch is the water closet, The 2 inch is for the shower and should have a p trap under the slab.( Pour water down should be able to see water) The other 2 inch is a drain for the lav and also would vent the water closet and shower. Use a 2 x 1.5 x 1.5 sant tee by the lav, 1.5 would then be the vent. Look for a vent stubbed down from the ceiling.

Note: Smallest drain line under slab is 2". That could be a roughin for a tub.

i would cut off the pipes 2" above the floor
stick atape measure down the pipe, and see if its a 90 or a trap,you cantell by the resistance to the tape
if it turns on a 90....or if it makes a j bend
the pipes are in a line.as if in a wall.i "assume" that the tub is not traped, sence there is no tub box around the pipe
and the pipes seem to be in a line,if the tub was traped,it would not be inline but offset..,so the toilet is not roughed in either..or it would be 12" away from the others [12" out of the wall]
you were left the drain and vent piping, but you need to bust concrete, for the toilet "arm" and the shower trap
on the three "..LOOK INSIDE THE PIPE FOR A TEE OPENING
that would be the toilet...but i doubt it is there
the 4" is a co..a end of run c.o

It turns out neither of the 2" pipes where trapped. I busted the concrete up this past weekend, installed a trap on the corner 2" (along with moving the vent) and plan to use that as the shower. I then moved the 3" pipe for the toilet 5" away from the wall (I will need this offset once the studs and drywall are in place). Thanks for all the input.

Now I have to fill the holes back in with concrete.