Baker would probably have some insights here that differ from mine, but I am trying to clear out the backlog of posts going into the holiday with the large, egg-laying rabbit.
1) Depends entirely on what you are doing. If I were training you, I would probably stick to one set of five at the moment instead of five singles.
2) I've messed around with this and if you are going to stick with a 3-day TM routine and you want to power clean, then I prefer deadlifts on the volume day. Five sets of cleans after five sets of squats and presses is awfully long. Many do not like deads on Monday because it makes Mondays so hard. However, it also sets things up so that you kick the hell out of yourself on Monday and then recover for the rest of the week. The intensity day is heavy, but over quickly and power cleans are like a reward after making the squats and presses. Deadlifts on Fridays tended to negatively affect my volume day squats. If you just cannot deal with deads on Mondays, try them on Tuesdays instead.
3) Worry about getting your fives going again and drop the high rep deadlift stuff. Deads are not a great conditioning exercise. Row, or push the prowler, or do some sprints (I think 400s are a decent choice) if you want conditioning work. High rep deads are good for tweaking your back.
The TM is tough. You need to have recovery in good order to pull it off.