Just keep it professional...Like you are and try not to think of it as you don't want to look bad...but as..you want to look professional.

I don't think this is a bad thing that you are cautious in this area...I do think you are overthinking it...it seems you have it down and don't have to think of it all the time.

You know not to act inappropriately with students.
You are the role model.
You are doing all the right things...and as long as you are adhering to the rules set forth in your institution you will never "look bad".

Contrary..you will look "good"...take some pressure off yourself....remember...you have trained for your position you are capable and trustworthy or they wouldn't have hired you...don't worry so much about what others are doing..unless it is totally inappropriate and then pull them aside and TELL them so....

Otherwise..you sound like a young kid..just getting used to the business world. Your not there to make friends..your there to do your job...and if possible set an example for the "kids" and others.