1) Not easy to calculate because of variations in transistor Vbe. Trip point depends on R1 and R3. Simulation shows that, with the values given, Q2 begins to turn on when battery voltage drops to 1V. Increasing R1 (or reducing R3) increases the turn-on trip voltage.
2) I don't know, because the internal circuit of the TriggerLinc (TL) is unknown. My circuit will only work if one of the TL sensor terminals is connected internally to TL battery negative (-). It needs three connections :- (i) from Bat to the TL battery positive (+), (ii) from Ground to - , and (iii) from Out to the TL sensor terminal which is NOT connected directly to + or -.
Using a multimeter, can you detect if either of the TL sensor terminals is directly connected to TL battery + or - (I would expect it to be connected to one or the other. If it's connected to + then we can modify the circuit to cope.)?