Is it appropriate to give your professor gift card as bday gift?

Nope . A thank you card after your class is finished is fine ... but if you’ve done well in their class that is all they really want

Yeah why not, tbh the minimum amount would be just fine unless they're a really good professor and you wanna treat them for being a star

No. Go to class. Do the work. Take the exam. Move to the next course. After the course is done then you can consider a friendship.

Much better than the gifts my students use to give me

Sure but the more conventional typical gifts is a mug

If you want a good grade, give him a beer.

Probably best to steer clear of that. There's nothing explicitly wrong but it could come across as improper by other students.

Generally It’s appropriate to give them anything you want

Why do you even know his birthday?

Sure

only if you really want his penis