@Ertai: I know you know, but you didn't fix it so I just posted the right way to say it for you cause there is really no point in teaching the people here uncorrect Japanese, でしょ？
In answer to your question: I'm not quite sure if your interpretation of ～てくれる is right or wrong... >_>; I'm sorry. I know, I'm really useless when it comes to explaining things about the Japanese language. >_< You'd probably be better off asking Mistress or Datenshi-san about this kind of stuff.
Oh!! And I finally realised there is a way to translate that sentence!!
(lit. That Japanese teacher is very skilled at teaching, and is easy to follow.)
And Ertai, it should be: 次の電車に乗らなければ、遅く着きます。
@ the game:
(lit. I recived a Japanese souvenir from my friend.)
Next: Are you not feeling well?