Mechanics questions

[SC Ump]

My opinion in blue.

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?
> That is my understanding.
2) If there are trailing runner(s), should the BU stay with them or help with rundown?
> I would help with run down, remembering that the trailing runners are still my responsibility.

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?
> I personnally do not consider a throw from the outfield to be the "first infield play." If I was the PU, I would consider it my call.
4) Same scenario, what if there are trailing runner(s)?
> Same answer (aren't there always going to be trailing runners, i.e. the BR?)

Situation C: Multiple runners, BU in C.
Batted ball caught in air, thrown to 1st for live ball appeal.
1) Whose primary responsibility?
> It depends on how many runners and where they are.
2) Same scenario, but only runner at 1st, BU in B?
> I believe BU has tag responsibilities.