pvc

Hi all, Not new to reading the forum, but new to posting. We are finishing our basement, and are now onto the bathroom plumbing. The shower drain and toilet drain have been roughed in underneath our foundation, but the sink is not, leaving us to best decide where to tie the sink drain in. Below...

I have a downspout buried drain pipe that was constructed with 3" PVC having what I would call "slip joints" with a "bell" end of a few inches on each 10-foot section. The pipe is marked PWPipe PVC Sewer Pipe ASTM .... One of the slip joints parted by nearly a foot so I'm moving one of the...

I wish to put a T into a short piece (5 inches) of existing 1/2" pvc that is fixed on both sides by non movables (wall valve and water tank input) . I won't be able to flex the cut ends in the pvc to slip the T into place. Any tricks how I can put in a T in this situation? Thanks.