The brides permanently change how a Senator feels about you. As long as you don't kill them if you choose to force the bill through, it doesn't matter if they say yes or no -- their affection really just offers a percentage change of them saying yes.
So it doesn't matter if you return to HQ, win or lose (again, as long as you don't kill).

And on the note of trying to force your way through, you can cheese it by not killing any of the agressive ones; rather you throw them into a higher level senator who voted yes, which won't affect affection.

1) The effect of bribes is permanent.

Using a phone to call a party only affects the next bill, I think.

2) Casting the vote or not doesn't change the effectiveness of your bribes.

You can use the "war funds" bill to bribe. It costs only 10 mana, attracts a lot of senator, and has such a negative favorability that you can precisely see if you have maxed your favor with the senators. Don't try to cast the vote, the bill will be rejected (even if it won't, it's not worth it). Fill your inventory with random crap from the store, bribe, repeat. A senator liking a given item is solely based on the rarity number.

3) Yes, bribing a senator also slightly increases your favor with the other senators of the same party.