Oh sorry about all the questions I just have one last one... :/
At the end of the email my friend said まってるね. Is this a spelling mistake of まてるね?

Nope. Yours is the mis-spelling.　:D

待ってるね = "I will be waiting for (something)."

待てるね is a question meaning "We can wait, can't we?", "You can wait, can't you?", etc.

待ってる is the colloquail form of 待っている, which is progressive.

待てる is the potential form of 待つ.

Keep asking questions.

To form て form of verbs, take what is left of the arrow and replace it with what is right of the arrow:
う、つ、るー＞って
む、ぶー＞んで
くー＞いて
ぐー＞いで
すー＞して

and the exceptions
来るー＞来て
するー＞して
行くー＞行って

TO the tune of Santa Claus is Comi' to Town:
utsurutte (you'd better watch out)
numubunde (you'd better not cry)
kuite guide (you'd better not pout)
su-shite (I'm tellin ya why)
suru shite, kuru kite, iku (santa claus is comin')
itte (to town)

That's the most hilarious way to remember てform I've ever seen. Thanks for sharing!

Other classes at UT were taught that way; I don't remember any way other than just learning it over the course of a week or so.

Yeah, I learnt just with rote memorisation and practice, but the way I learn, i find mnemonics really helpful.