Mechanics questions

[CecilOne]

Two umpire system:
Situation A: PU has 3rd, but we have a rundown with PU at HP end and BU at 3rd end.
1) If the tag is made at the 3rd end, is it then the BU call?
2) If there are trailing runner(s), should the BU stay with them or help with rundown?

Situation B: BU customarily or by pregame has the "first infield play",
but it's a throw from the OF to 3rd.
3) Is it then the PU call?
4) Same scenario, what if there are trailing runner(s)?

Situation C: Multiple runners, BU in C.
Batted ball caught in air, thrown to 1st for live ball appeal.
1) Whose primary responsibility?
2) Same scenario, but only runner at 1st, BU in B?

If I can look these up, feel free to tell me I'm just being lazy. The obvious answer is verbal communication between umps at the time, but I'm asking if there are prescribed answers in any sanction.