There are three main event types in rotation in our version of PPS. Elite Guard (current event), Coliseum and Gambit.
In Coliseum you build a deck of 5 cards and have head-to-head matches against other players' decks. Each match costs 2 focus. If you win, you get coliseum tickets (the number of which depends on the difficulty tier of your opponent). Every 5 tickets allow you to spin the coliseum gacha, which rewards items.
Gambit is an exploration type event. You spend stamina to progress through stages. At the end of each stage you're presented with the chance time-like 6 choices. If you pick a "right choice", you advance to the next stage. If you pick a "wrong" one, you have to start that stage over from the beginning. The number of right and wrong choices depends on the stage number, however, if you fail a stage multiple times, the number of right choices increases. There are 100 stages in the first phase and another 100 in the second.
Randomly, you'll encounter bosses through the exploration. These bosses will require either 1, 2 or 3 focus to fight, and are automatically defeated as long as you have enough focus (SED doesn't matter). 1-focus bosses will drop either a pink box or a pink key, 2-focus a silver box or silver key, 3-focus a gold box or gold key. You also get pink keys from buying nGachas during the event, silver keys from buying rGacha (with nutaku gold) and gold keys from eGachas (again, with nutaku gold).
You cannot open any boxes you find yourself, instead, any boxes you find are automatically broadcast to everyone on your friend list. If they have the appropriate color key, they can unlock it and you both get an item from it. Since pink keys can effectively be bought with pero, it's usually a mad scramble to open pink boxes and they rarely last more than a few seconds.