A) There is no registry.
The only thing remotely resembling this is the APT database that keeps track of programs and dependencies. This pretty much takes care of itself. The commands:
apt-get autoremove and
apt-get cleantake care of the other parts of it that aren't automated.
B (1) Defragmenters aren't necessary either. Your disc is, for all intents and purposes, always defragmented because of the way the various disc formats deal with information.
I'm going to invoke my OpenSource heart here and not reinvent the wheel. This guy, whom I consider to be a SuperGuru, largely because he's able to communicate complex ideas in very clear ways, explains why better than I could.
http://geekblog.oneandoneis2.org/index.php/2006/08/17/why_doesn_t_linux_need_defragmentingAlso, even though some degree of fragmentation may occur, it doesn't matter in most cases:
http://geekblog.oneandoneis2.org/index.php/2008/11/13/fighting-fragmentation-on-linuxThe moral of the latter story is that Unix, Linux, and OpenBSD (and by extention Macs) approach disc management in an entirely different way than Windows that doesn't require a lot of manual maintenance.
B (2) Most distros put into their boot sequence a check dealing with file system integrity. You'll notice this clearly if you just cut power to the machine to shut it down rather than go through the logout sequence. One of the first things that happens when you start up again will be a filesystem integrity check. It will NOT be clean, and it will fix itself.
Also, the check includes a timing check. If the disc has gone a number of days (and I forget what Ubuntu/Mint sets this as) without having its filesystem integrity checked, one will be done automatically prior to boot. You'll notice this at the time as the system taking a LONG TIME to boot, but don't worry about it, it's normal, and it takes care of a lot of the issues that arise with hard discs.
C) You may not be aware of this yet, but you have what are called cron jobs running in the background that are set by the distro developers who put them there to run at periodic intervals and clean up a lot of stuff. Where you'll get clutter in a Linux system is with the logs and files in /tmp. Several cron jobs are set by default to archive stuff on the /var/log directory and store it in a tarball (an archive made with the archiving program tar, sorta like zip or rar).