Remember in English, the "tense" is very important... past tense, present tense, etc. It's important for a lot of words, and for most sentences. You can say "Please correct me" but you can't say "Please correcting me". You haven't been corrected yet, it will happen in the future. You can say "Thanks for correcting me" but you can't say "Thanks for correct me". You have already been corrected, it happened in the past. You can say "That nice lady corrected me" but you can't say "That nice lady correct me". I'm not sure how to explain this, but it's true :)

Thanks for correcting me.

No, "Thanks for correct me" is wrong, your friend is right. "Thanks for correcting me" is the right choice.

Thank you so much Rahul. you taugh me a great way. Thank you.

The verb used after any preposition, must be in -ing form. Therefore, "Thanks for correcting me" is right.