As a student, is it fine to trade in stocks with a broker?

I started trading when I was student, so my answer to this question is a definet YES.
As a student you dont have any financial burdens or family responsibilities on your shoulder so you can experiment in this field without worrying much about your career.
I personally feel student time is the best time to start trading and analyse yourself whether you are capable enough of taking it seriously or if it is not your cup of tea. When I started trading, I lost money in the initial stage but I kept on trading by adding more funds and by the end of one year in trading world, I was earning far better than the best package of my college.
I would strongly recommend you to open a demat account and go ahead and enter to the trading world, even if you fail here, you always have your degree as a rescue, and if you do well here, you can start making money on your finger tips.
After getting into corporate world due to lack of time and increased family responsibility one can never pursue their interests, thus keep experimenting as student.

Hope my answer will help you.