A few days ago I talked about the terminology confusion in SalesForce between apps and packages.The reason I was digging around with this is because I was trying to figure out how to update the apps in SalesForce.
As far as I can tell, there is no auto-update system for apps/packages. Some apps do implement their own form of updating. The Non-Profit Starter Pack (NPSP) is one. Others have an updater built into the app, like Click & Pledge (it's in C&P Settings > About C&P Apps; click Sync for Updates).
But for most, you just go back to the SalesForce AppExchange, find the app and check its version against the one you have installed. If there is a more recent version, simply go through the process of installing it again.
Also, the Installed Packages setup page is where you go to manage licenses for any third party apps. We use Apsona and S-Docs, and both only allow 3 people in our org to access them. This is where I go to change who gets access.
Also a tip: If you enable the Organization Admins Can Login as Any User feature, then admins can log in as one of the users who has a license if they ever need to do something with that app. It's a good backup for when people are out of the office or otherwise not available. Of course you could just reassign the license temporarily and then assign it back when you're done.