You shouldn't worry about what your level is (unless you've already been to 30, and are on a smurf account). You should worry more about getting the experience from legitimately playing the game all the way until you're a high enough level.

IF you've already made it to 30 before and experience is something you've already got, still no. There's no way to level up quickly besides playing and winning more often.

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Only way to level up quicker is go buy some RP and use it towards XP boosts all the way to level 30. No other way to speed level.

Unlike IP, your XP per match is based off of the kills/assists you get.

So, if you carry and get a lot of kills each match, you will get more xp than if you were a supporter.

It will still take quite a long time though.