Unless you need specific new features in Natty, I would recommend keeping your server on it's current version and continuing to apply security patches and updates.
Then, spend time reviewing Natty yourself and seeing how much work it will be to migrate to it. Migrating to new releases can be a big piece of work, but it depends on how many packages you have installed, how much customisation you've made and what kind of customisation that includes. There's no simple answer.
If it was a Desktop, it's less of an issue, but since you say it's a server I would take a cautious approach.
So, stay at your current version. Take a good look at the Natty release notes, consider how much you've configured / changed on your server and then do the upgrade in your own time, at your own speed, when you can live with the downtime.
When I last did this (with Debian), I built a new virtual server (very cheap, only needed it for 2 days), built an environment which matched my current live server and ran through the upgrade. Learned those lessons, and then applied them on the live server to make the upgrade quicker and less problematic.
As for your other question, you should be applying security updates to your Ubuntu server on a very regular basis, certainly weekly if not more often. Security updates shouldn't impact any functionality (but you can never be 100% sure). For anything other than security updates, on a server, you should upgrade only when you need required functionality or your current versions no longer receive security patches.