Rotation happens once a year normally after worlds. The most recent one just happened in September, so the next shouldn't happen till next fall. For the past few at least roughly four sets have rotated out of standard. (Currently Primal Clash to Evolutions) To my knowledge, no sets have ever rotated out of Expanded. (Currently Black/White to Evolutions) It's possible that once Sun and Moon comes out expanded will drop BW, but I'd leave that up to a more experienced player to speculate on. Standard normally keeps roughly two to three years worth of sets, where expanded I believe has seven at the moment. Don't quote me on the expanded years though, I'm mostly a standard player myself.
New sets in America come out roughly every three months.
Out of the current two to three years of sets in standard format, all of them are used in competitive play, it's not the set but the cards in the set. For example, in Roaring Skies (ROS) set you can get Shaymin EX. That's one of the most powerful cards in the current format and used in just about every competitive deck. Once you have that card, do you need more ROS packs for competitive play? Maybe, maybe not. There's a few deck-specific staples in the set, like Rayqueza EX, but if you don't plan on playing Ray then you don't need those cards. Using another set like Break Point as an example, you can get Greninja Break. You obviously need Greninja Break in order to play that deck. What I'm trying to say is while each set may have a few cards you need, all competitive decks will use cards from a variety of sets.