How can I get my students to sign up to my Moodle site?
Look at how to set up email based self registration.
How can I suspend a user's account?
Tick the 'Suspended account' checkbox on the edit profile page.
Can Moodle send a notification e-mails automatically to a new user when an account is created for them?
Not at the moment with core Moodle. See Tracker items MDL-19390.
There is a work around. If you create a CSV for your user, and OMIT the password field a cron job does get triggered and an e-mail is sent to the user. The text of the e-mail is customisable by an administrator in the admin settings. See: https://docs.moodle.org/24/en/Upload_users#Fields_that_can_be_included
How can I log in as another user?
This is normally only allowed for administrators because of possible security issues. Click on the user's profile and then look in the Settings block on the side. Click the link there.
Note that when you have finished, you will be logged out and will have to log in again. This is deliberate, again for security reasons, but you will be returned to the page you just left.
How can I prevent users from editing elements of their profile?
You can lock user fields from Settings>Site Administration>Plugins>Authentication>Manual accounts
The search box for users is limited to 100 displayed users. Can I change this?
For a discussion on changing the code, please see https://moodle.org/mod/forum/discuss.php?d=186777 For the teacher request see https://tracker.moodle.org/browse/MDL-36395