From grammatical point of view the first sentence is not correct. The second sentence is the only right variant.

The meaning of the two sentences is exactly the same. You would hear (1) more often. In spoken English, you would also hear it this way: "I'll help you learn English and you help me learn Turkish." It seems contradictory because of the differences in tense, but that is just the way people would say it.

I agree with Helen's comment. However, I prefer to use the formal grammatical form; which is the second sentence.

In the first sentence, "help" works as a causative verb. The difference between "help you learn Turkish" and "help you to learn Turkish" is so tiny we simply don't worry about it. For a natural phrase, Frank has already given a good example (and yes, it is very grammatically sound). Your sentences seem to be stating a general fact instead of making an offer. By the way, please pay attention to capital letters.