All of your concerns really depend on the application. Just because a website offers an extractable download instead of an installer does not mean this version will put less clutter on your system. Essentially it is the same content as the installer although it gives you the choice of where to extract it to, and comes with an uninstaller. Most uninstallers attempt to delete the associated application files, then delete themself (See self-destructing executables). Most zipped programs will still put their information in the registry.
Updating methods would depend on the application itself. Some programs will automatically download an updated version of application files and overwrite the existing main executable, others (extractable) can be updated by downloading and extracting the newest archive.
I don't see much of a difference between installing software or extracting it to your machine. Most uninstallers these days do a good job of deleting application cruft, but a lot still leave things behind in temp folders and your registry. Likewise, programs which are simply extracted can also use your registry and temp folders for workspace. Sometimes the things left behind are for the better, such as your personal settings for a browser you may reinstall some time. I know it's saved me more than once.
Personally I prefer installers as they require much less management. No cluttered desktop filled with extracted programs that you need to delete and move around.
If you are really concerned as to what a program is doing on your system, take a look at Process Monitor from the Sysinternals guys. It can be as simple or verbose as you want it to be by making use of filters.