How does the Battle Booster work?
Solution 1:
It's 500 minutes of matches.
The previous version of it lasted x number of days, which meant that you had to use it when you knew you could play a lot. The new verion is much better in this respect, just use it and none of it goes to waste.
The bonuses DO stack if multiple players have them, from both teams as well.
Solution 2:
Once you've used it you will have 500 min in-game of battle bonus. The countdown decrease only when you are actually playing and no longer expire at a given date which is much better because you wont "lose" any battle bonus time. If multiple players in your party have a bonus active, its cumulative thus it has no impact if you decide to use it later or not.