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what champions do you have?
so basicly, there are a few champions available in a rotation that changes every week - so every week you have other champions you can test or play with. by playing you gain IP (influence points) which you can use for buying other champions.
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why can't you always select the same one?
as already said, there's a rotation that changes every week. if you like a champion, then you can buy them. some are cheap, some are expensive. they cost either 450, 1350, 3150 or 6300 ip. if the champion is really new, they cost 7800 ip (in the first 2 weeks)
and you can't always select the same one because every champion can only be once in every team. later you'll find game modes where the champion can only be played once in every game.
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what are runes?
"A rune is an enhancement that the summoner provides for their champion before a match on a field of justice begins to augment the champion's abilities."
look over here for the full article:
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and is there any specific lane a specific champion should go?
well, kinda. first take a look at this to understand the different roles which are in the current meta (basicly, meta is the way you play this game at the moment) =>
but there's no rule which says you are only allowed to play some champions on this and this lane, but there's some champions which have useful abilities for some roles.