Sorry to say, but I don't really see much in the photos that will be helpful.
The first pic shows what looks like a 3" drain right up against some studs (and some nicely painted toes :wink

, it should be scoped w/ a camera to determine where it goes & what it could be for. Then the studs will have to be moved the appropriate distance (12" from
finished back wall & 15" min from
finished side wall).
The second pic shows what looks like 2 cold water lines, a hot water line, and a what seems to be a 2" drain transitioning to 3" drain with a cleanout. You cannot tie into the threaded cap for your sink drain, but you might be able to T in above. How high is the joint where the 2" drain enters the top of the cleanout fitting from the floor? How will the floor be finished?
The third pic shows what looks like a 3" drain (is there a toilet above there?) and a hot & cold water line.
Perhaps a clear, uncluttered pic showing the entire area would give us a better perspective of what you see and will allow us a understanding of what you're working with/against.
Andy.