For the teachers or tutors: do you put your job on Italki on your resume? Have you ever asked one of your students to be your reference, is it acceptable or does it cross a line?
On italki I'm freelance, not employed. I wouldn't ask a student for a reference but if I needed a sort of testimonial I think I'd simply say, "Have a look at my feedback on italki."
Fortunately as I am retired from the world of real work (I'm part-time, and mostly retired!) I don't need references. But I can imagine the situation of needing some kind of teaching testimonial. I'm going to do voluntary work in India - italki may help me establish my credentials. Having a profile, and some years of feedback, will help.
Teachers on Italki are considered "Independent Contractors" and don't exactly work for Italki. Italki is a platform that allows me to post my teaching profile, make my own rates etc, but is not my employer. Thus, I have on my résumé that I am a freelance private language tutor. I work with students from various sources, not only with Italki.
The reference question is a good one. They could write a testimonial for you. I seem to recall a student offering to write a reference, but I think she offered without my asking. I think it's best to get some other professional contacts to write references.