I know that we need to win 2 of 3 games to rank up, rigth? like form silver 2 to silver 1. Is it possible to rank down? like silver 1 to silver 2? There any matches that we need to win to stay in that rank?
Demotion happens when your current League Points reach 0 and you lose enough games to get demoted. When you are demoted you go to one division below your current and get 75 LP in that division e.g. if you are in Gold II and get demoted you will fall to Gold III and have 75LP. There is also a demotion immunity grace period for several games, in which you can't get demoted to a lower division, which activates when you get promoted to a higher division. This is to make sure you don't fall to your previous division due to bad luck. However, one will demote out of Masters into Diamond I after playing at least 3 games, then losing with 0LP.
During server issues losing a game and getting "Loss Prevented" prevents demotion and will not count as a game for Promotion Series - you won't lose them due to that game.
As of Season 4, it is possible to be demoted from a tier. If you are in division 5 of a tier and your MMR drops an entire tier, you will be warned about possible demotion. For example, a player in Gold V would receive a warning upon reaching Silver V MMR.