Nope. App Store requires changing app to add app store features, submission, etc. Not just a simple update site.
Yea. People don't even begin to realize how things work around here.
The biggest thing to think of in this regard is that Apple has receipts stored for all applications you've purchased on the Mac App Store. It can link up one to one the various applications that you've purchased and handle whether those are installed and are in need of updates.
If you haven't purchased the app from the Mac App Store then there's no way in hell they could just say "oh yea, you should get updates for this application"
For one, there's no such thing as "activation" or "serial numbers" on the Mac App Store. They're encrypted, signed applications. Just like the iPhone and iPad stores. This means if the app is installed, it's a purchased app.
How would developers feel if Apple just recognized apps that were previously installed and updated those to unlocked fully functional apps regardless of whether they were purchased or not?
Applications you purchase from the Mac App Store are completely separate from those purchased from the developers website. The executables are very different.
Do not expect applications to update in the Store. You did after all NOT buy them from the Mac App Store right? So why would the "Mac App Store" update applications you haven't purchased from it?
Right... put 2+2 together now and try to grasp the concept.
As for how the apps are installed? Well, they're installed for you automatically. Just like the iPhone and iPad equivalents.