Mary might know more about this, let's see.
I would have used the Library phone number.
You can only log into you moodle as a student if you have the enrollment key for the course of interest, or if the administrator (meaning you) manually creates an account for the student. How did you try to "register?"
To experiment, you should go into your MoodleCloud account (as administrator), and then create a new student for yourself. You will need a unique email address, but I think you can fake one. Then add this student to a course, and finally log in as the student. You can do this as much as you want with fake email addresses. But realize that your moodlecloud course might try to email something to the fake student. In my case, I have around a dozen or more email addresses, so I can use any of these for testing. I bet you have at least a half dozen (you might need to remember.) If not, create several gmail and/or yahoo email addresses for yourself. Make sure to write everything down so that you can remember.