Thanks for the FAQ suggestions. I've updated our About page and FAQ to touch on both topics.
As for your questions:
1) No install games typically don't create registration files so they are sometimes "cleaner". They also don't create desktop shortcuts or program file folders so some convenience can be lost. There's really not much of a difference though. One isn't inherently a better or worse version. Most installers just unpackage game files through an .exe. With the no-install games it's effectively done through a RAR or ZIP file.
2) The serial check will either connect to an online server to validate a key or check some internal code to validate. The way it's added can vary per game, but we don't sell anything that requires more than that (i.e. no always online games, etc).
3) It varies. Some games require online checks and some don't. Again, the online check would happen only once (during install or your first run) and would not need to be checked again. So once the key is registered you can play the game on the offline PC forever.
4) Yes, it might not be the final version. We're working on our mailer system now which will include messages going out to customers whenever we update game files. This could include adding extras, adding patches, or updating the installer itself.
Let me know if you have any other questions.