The people you'll be playing with are as new as you, there's nothing to worry about.
Peeling is when you get the enemy off your carries (The squishy damage dealers) Alistar does this by headbutting, knocking the enemy away. A bad alistar headbutts the enemy carry out of the fight, effectively peeling his teammates off of them.
Heimerdinger is usually played by Brazilians, who tend to be godawful at the game. He's also a really irritating champ in general.
Irelia needs lots and lots and lots of gold, and is only good when she can get a solo lane. Gangplank will steal her gold or they'll share and both be useless.
Morde is basically a meme, and lots of irritating jackasses play him. His ult, if it kills the target, turns them into a ghost taht fights for you. Ghosting a carry wins games. Ghosting the tank is something idiots do.
Nunu is an awesome counterjungling (Killing enemy jungle creeps and otherwise messing up the enemy jungler) but free week nunus won't counterjungle. His ult is really strong but easy to interrupt. Starting a fight will waste it.
Rammus can roll really fast at people and stun them for easy kills. Free week rammuses will hit minions and waste it.
Twisted Fate can teleport around the map and stun people. Free week twisted fates use it to suicide.
Urgot's ultimate switches his place with an enemy. Amumu can snare your entire team for like two seconds. Ulting amumu will lose your team the game.
Zilean's ultimate gives you an extra life. Free week zileans don't use it on people who need it.