Answering questions and correcting notebooks is a great way to get noticed: 2 of my first 5 students were people whose notebooks I'd corrected. You might want to lower your rates for your first month or so: $ 20 for a brand-new teacher might be a bit scary, but more people would be willing to try you at $15. After a month, or so, once you've established a reputation, you can begin asking for a higher price. Good luck, and welcome to italki.
Your profile is visible for students and they can book lessons.
As an experienced student here, I think you need to improve your introductory video.