Welcome.
First of all, support in League does not mean the same as support in Dota. In Dota, you put every hero somewhere on the carry-support spectrum, that 1, 2, 3, 4, 5 role numbering system. In League, "support" is a specific position, one out of five positions. The support position itself is varied between tanks, enchanters, and mages that deal damage. Only enchanters (primary healers and shielders) are exclusive to the support position, you'll see the other ones in other roles but they will not be called a support even if they perform the same function in the support position or in the top position.
In Dota you typically call a carry someone who will deal damage by right-click attacks, but in League all mages' and spellcasters' abilities will scale and can carry a game.
Instead of the offlane and safelane notation, we say top and bot lane, and it is symmetric; there is no difference such as Dire offlane vs Radiant offlane are on the other side of the map. Typically, a marksman and the support goes botlane. You typically have some sort of roamer or control heavy mage or assassin in mid lane. You have a range of bruisers, tanks, marksmen and mages in top lane, and a similar range for the jungle.
That's another important part; in League you always have a jungler. Well, except for the games right in the beginning like for you right now when you are starting. Jungling requires a bit of experience of the game, as well as a couple of runes. In low-level games you often have two people in the top lane instead.
Yeah I just had a good Kha on my team, he did tons of damage. It seems legit.