I'd like to finish my basement bathroom that has already been roughed in. However, I'm having some trouble figuring out the pipes. I've attached picture that should help. I know that the 3.5 in diameter pipe is a radon vent. the 4.5 in stub coming out of the floor is the toilet drain. and I think that the 2.5 in pipe in the wall is the sink drain/vent. However, there is another 2.5 in stub sticking out of the concrete in the wall. I believe this is for a shower/tub, but how do you connect to it? Also, will it use the same vent as the sink and toilet? Some verification and help would be appreciated. Thanks.
This looks like a typical wet vented bathroom group. You are right, the "extra" pipe is for a tub and it's is almost certainly vented, along with the toilet, by the 2" pipe that will also serve as the lavatory drain. After installing a sanitary tee to catch the lavatory, you will continue this pipe vertically to become the vent. The other possibility is that the drain pipe for the tub is buried under the concrete and the pipe you see is an individual vent, but I'd bet on the first possibility.
There should be a 2" pipe stubbed down through the basement ceiling to vent the pump can. You can connect the bathroom vent to this pipe, along with the pump can vent. You may or may not also have a pipe already connected to your drain line overhead to receive the discharge from the pump. If not, you will need to install and connect one when you install the pump.
As for the tub drain, it looks like you will have to break the concrete to connect the tub. This isn't too unusual. Many times the plumber installs a box out for the drain and the concrete finishers remove it. Or there may be just a thin layer of concrete over a box out. Bang around with a hammer and see what happens. When you get the floor opened up, check for a p-trap on the tub drain, it needs one.