Team Fighting & other questions

One day I decided to purchase and give a shot after I saw someone playing her in ARAM do really well with her. The first time I played her it was awful since I didn't really know how her combo went and was mostly experimenting with her rotation. That game went fairly bad in terms of KDA, however, now that I know her rotation I've noticed that I tend to go positive in most of the games I use with her. I can normally win in a 1v1 and the occasional 1v2/3(depending on the champs I face). The thing I've noticed though is that when I play a game, my team doesn't know how to initiate team fights all that well, and the enemy team either initiates them or I will sometimes be the initiator(bad decision, I know). When team fights occur, I find myself using E to go into that fight, W to get off some AoE damage and then using her R. During the ultimate, I tend to get focused down very quickly and just get murdered. When would be the best time to go in with her on a team fight? What type of champ should I focus down(ADC, APC, Tank, etc.)?

Another thing I wanted to ask is about MMR and ELO. I know that MMR stands for Match-Making Rating, yet I'm not sure what ELO stands for yet. Could I get a little insight on that? xD

Since I main Mid lane champions, I decided to secondary main Support on the occasion that someone gets mid before myself. I purchased Janna and do reasonably well with her and would like to try out a couple of other support champions, what would be some recommendations from you guys? For the games that I can't get both mid or support roles, what would be some beginner level ADC/Top Lane/Jungle champions to use?

Also, is there anyone that would like to become my coach for 5v5s to see how well/poorly I do?

Thanks in advance. :3