Basement Bathroom

[PLCControls]

I am beginning to start finishing my basement which will include a bedroom, living room and 3/4 bathroom with a standup shower. I am no plumber by no means but i do know a descent amount about construction and electrical. the house i am living in they roughed in the bathroom when they built the house in 2000. i understand some of the plumbing but not all of it. I see the 3in pipe is going to be for the toilet and its plenty far away from the wall (about 15in), the 1 1/2in pipe to 2 in next to it i would assume is for the sink drain. Am i correct so far? the other 1 1/2in pipe to 2 in is for the shower drain im guessing? Would i have to tear up the floor and tie in a shower drain to this stack? None of the other fixtures upstairs drain into either one of these pipes. All the fixtures upstairs drain into the main 4in stack running through the house. Also can anyone tell me what the purpose of the small 1 1/2in pipe is coming out of the ground in the corner. Any input, suggestions, ideas would help out a ton. Thanks in advance.

 

[PLCControls]

Is anyone a plumber on here or just in the same boat as me? Lol did I leave out information that is needed to help me out on this?

 

[frodo]

This is what i see

 

[PLCControls]

That's makes sense I like to over complicate things when looking at stuff. My next question is one the drain for the tub is there standard distance it needs to be set away from the back wall? Or is it different for every tub? I didn't know if there is a standard or if most tubs are the same distance