To answer your question as stated, I would look first at an event loop, which in my preference would be AnyEvent. You might particularly consider the section in the tutorial headed Timers and other event sources to implement your 30-minute schedule.

The second function is for the script to send an "I'm alive" email every 30 mins or so

That, however is the intriguing part. I cannot think why you would want this - it sounds much more likely that you'd want to be alerted every 30 minutes or so if it wasn't alive - ie. in normal operation it's quiet, but when it is not running you receive an "I'm dead" email.

Either way the trivial solution is not a Perl one but an O/S one: a cron job to run every 30 minutes which checks the process is running and sends your email if it is (or is not, as preferred).