ενα πουκαμισο is a button down shirt, right?
Yes, that's right.
Why is this wrong?
I took to Google and found that the third-person singular conjugation of "φορώ" is "φορεί", not "φοράει". Are they both correct? Are they used in different circumstances?
Both are correct and both are accepted. You can use either as you wish as long as it's consistent.
I wrote "φορά" instead of "φοράει" and it was not accepted. Can you please fix this?
"φορά" is already included. Maybe you had another error, such as the wrong article. It's "ένα πουκάμισο". Or some other error.
Maybe, I will check it again.
This reminding me of the Arabic 'qomis' means shirt