Can admins create new accounts without passwords?
There is a module that does this.

Check out Generate Password.

It introduces this additional setting in Configuration » People » Account settings:


  Users may enter a password on registration. If left empty, a random password will be generated. This always applies when an administrator is creating the account. 


Then, when creating the account, leave the password field empty, but make sure you also check this checkbox on the "Add user" page:


  Notify user of new account 


The result of these two settings is that the module generates a random password when the administrator creates an account, and the user is sent an email with a notification about the account and prompted to set a password in the one-time login link that is included in the notification.

If you want to learn how it is done, read the source code.