In terms of the events, I'm currently only really counting the GBA games. In terms of timeframe, the events of Dark Dawn either haven't happened yet, or are happening as we go about the story. I may, at some point, decide to say "AND LOOK WHAT JUST HAPPENED ALL THE WAY OVER THERE!!!"
But that'll be decided later. As for your questions:
1. Weapons: I suppose stuff like daggers and spears are fine.
2. Animals: any sort of real-world animal is fine, within reason (my character, Gerard, has a lion). It'll be hard for us to go around doing things with an elephant in tow.
3. Age: 18+ is preferable. I look at the League as essentially a type of boarding school with all sorts of age ranges, but you don't exactly get jobs with the school until you've graduated higher levels. Age would denote experience and power.