"Do you have any idea why verification emails are not being sent?"
that can be for a number of reasons.
First, are you testing locally? if so that won't work for the emails, unless you have a SMTP server installed which is not a part of most local testing setups. you will need to test on the live server.
next thing to look at is the Insert behavior, is that set to redirect after the record is inserted? if so, that will prevent the email from sending. the redirect should be done in the email behavior.
if it's still not sending the email:
Who is your host?
Depending on your host, you may need to set certain options in Universal Email.
Some hosts will work if you leave the SMTP Server setting on the Email Server Tab blank, others will require that you enter the SMTP server address.
Some will work using the standard Mail protocol, other will require that you use the Pear Mail for SMTP, some using Pear mail will require authentication.
Some hosts may require that the from address being used be a valid email address for your domain. Some may require that the option to include the from Email address be passed as an extra parameter.
To be successful with Universal Email, you will need to know the requirements of your host for sending an email using a PHP script.
Also, double check your Spam folder, it is possible that the email is being trapped as spam.
As for only saving the random string, double check the insert behavior again on the registration page and make sure the columns are bound to the corresponding form elements on the registration page.