Every once in a while with the correct outfit (s) is very nice. I've seen classmates do it and I found it very nice. I've worn dress shirts, pants, and dress shoes to class. A lot of girls and even guys made sweet comments. So, do it especially if YOU want to.
No, if you want to wear them to class then do so. This one girl in my class last semester always wore heels, though I think she was either just coming from or going to work after class based on how she was dressed.
No, you can find some good casual clothes to wear with them.
There's nothing wrong with wearing what you like, just know, people are GOING TO HAVE OPINIONS. Question is, can you not let them get to you, and still wear them anyway... I can't answer that for you, since, I'm not you