Certainly! Here are some suggestions for checking the sentences:
1) "What factors can have an influence (play a role?) on the way we dress?"
This sentence is grammatically correct. However, you can consider adding a comma after "influence" for better readability.
2) "Are you fashion conscious? Have you ever been to a fashion show?"
These sentences are grammatically correct.
3) "Do you belong to any fashion conscious (?) teenage group? What sort of clothes do you like wearing? By the way, what are you wearing today?"
The first sentence seems incomplete or missing a word. You can rephrase it as "Do you belong to any fashion-conscious teenage group?" The second sentence is grammatically correct. The third sentence is grammatically correct, but you can consider adding a comma after "by the way" for better readability.
4) "What would you wear if you were invited to a New Year's party?"
This sentence is grammatically correct.
5) "Do you like your physical appearance (Are you satisfied with yourself?) or do you wish you were different?"
This sentence is grammatically correct, but "different" should be spelled as "different."
I hope this helps! Let me know if you have any more questions or need further clarification.