Nekem tetszik így, ahogy írta :) (I like your simple speaking-style) Amúgy így helyes stilisztikailag: "Szia, Amandának hívnak. Amerikában élek, jelenleg tanulok." (Theese are the perfect sentences) Don't give up! We really like your attempt!

Hey! Amanda i can teach you hungarian if you want, and hopefully you can teach me something about english:), i have facebook and skype, waiting for your reply, and sorry for mistakes

Szia Amanda! Well done! As others before me have already said it, you did a great job! Maybe, just to sound a bit more natural, I would change the word order like so: Szia! A nevem Amanda, amerikai diák vagyok. Köszönöm, hogy elolvastad. We are looking forward to seeing more Hungarian from you :)