Alliance Tournaments run in three phases: an Event Phase where members complete tasks for points, a Rewards Phase where the alliance's final rank pays out, and a Results Phase where the alliance gets promoted or relegated into a league bracket. Your alliance needs to be Level 2 to enter at all. League Events layer on top of this once you're placed: a shared task board serves the whole alliance, each member can only claim a limited number of tasks per day, and claiming a task removes it from the board for everyone else and replaces it with a new one -- so harder tasks (worth more leaderboard points and Alliance Tournament Qualifier Credit) get contested. Rewards can take up to five minutes to land after the event ends, because promotion/relegation has to resolve first.
The Surge is a short, sharp alliance activity: a G7 player (Ops 71+) with 100 Veilshards activates a Hostile Spawner in an eligible Surge system, and for the next three minutes any alliance member -- any level -- can pile in and fight the hostiles that spawn, which get harder as the clock runs. Scoring rewards both the alliance's combined total and each player's individual contribution, with the player who started it getting a bonus for doing so. If you're below Ops 71 you can't trigger a Surge yourself, but you can still join and score in one your alliance starts -- the level gate is on starting it, not on participating. Rewards come as Surge Fragments (refined in the Support Refinery), plus progression materials for specialty ships; G7 participants specifically also earn Primordial Plasma, needed for high-tier G7 Combat Tree research.