[aki11]

I wrote "おてがみありがとうね。" to thank them for the notes first. Would "tegami" be appropriate?
-Yes. It's correct and appropriate. also the "ne" at the end is. It adds a feeling of kindness to the word "ありがとう". At least I feel so.

Also how could I say thank you for the letter and picture (drawing) instead?
-You can say "てがみやえをどうもありがとう。"

Next does this make 100% sense? "えいごがすきになりましたよかったです。" (to say I am happy that you started to like English)
-"えいごをすきになってくれてうれしいです。"

Also "えいごがたのしんだよかったです。" (to say that I am happy that you enjoyed English)
-"えいごをたのしんでもらえてよかったです。"

Also "いつまでもがんばってください。" (Please always do your best)
-"これからもがんばってください。"

Also "バスケとおにごっこをしてくれて、ありがとう、とて� �もたのしかったですよ。" (to say thank you for playing basketball and onigokko with me, it was lots of fun)
-There's no need to fix!

Also "わたしもにほんごをがんばります。" (to say I will do my best to learn Japanese too)
-"わたしもがんばってにほんごをべんきょうしようとお� �います。" (I think this is more natural expression for Japanese.)

And "ありがとう、カメラマンをがんばります。" (to say thank you, I will do my best as a photographer)
-"ありがとう。カメラマンとしてがんばります。"

And a more challenging one, one of my students wrote "外国の人にあたらせっきょくてきにはなしかけてみた� �いとおもいます。" and I would like to reply that it is great that he has found interest in foreigners. Or maybe any other suggestions for replies?
-"外国の人にきょうみをもったのは、すばらしいとおも� �ます。"　(I'm not so confident.)

And finally "しんせつなことばありがとう。" (to say thank you for your kind words).
-"しんせつなことばをありがとう。"　

I wish this could be your help.