The official's manual covers this pretty well, although in your description it sounds like your association has the U and LJ positions flipped, so you would need to look at the typical LJ responsibilities in the manual since the LJ is typically on the 50 (R's restraining line) and the U is usually further down field on the same side. I don't actually have the manual handy at the moment, but basically the BJ should move to the middle of the field after the ball goes down field and he will cover deep returns to the goal line. The official on R's restraining line (U for your case) should move slowly towards the kick and then be ready for a big play up his side of the field at which point he will have everything up his sideline. To directly answer your questions
1. The official on R's restraining line (your U) should move slowly towards the ball and watch the blocks ahead of the returner, or around the action if it's a short kick in his area. Once the run starts to break, you basically treat it like a running play and cover action to the goalline as you typically would. The difference here being that with your alignment the U would basically have the LJ's typical coverage (sideline and pursuing to the goalline).
2. No, definitely not in your alignment where the U is on R's restraining line. Whoever has R's restraining line (normally LJ) is responsible for the sideline to K's goalline and the L is responsible for the other sideline to K's goalline.
3. The BJ should be in the middle of the field. The flanks should have sideline coverage to the goalline while the BJ will have the goalline. On a run along the sideline, the BJ should make eye contact with the flank on that side to verify that the player didn't step out of bounds before signaling TD.
4. The flanks that are furthest up field (it sounds like you guys have the U furthest up field for some reason) are responsible for covering the sideline. They won't beat the returner to the goalline on a long run, that's the BJ's job in the middle of the field to beat the returner to the goalline. The flank's responsibility on this is to pursue and make sure the runner doesn't step out of bounds, as well as the usual coverage stuff like watching for bad blocks in his area.