64 bit builds
From MozillaZine Knowledge Base
You can run a 32 bit version of a Mozilla application using a 64 bit kernel (Windows 7 x64 etc.) though a 64 bit version "supposedly" increases performance. However, it is not obvious whether or not a 64 bit version increases performance.
Unless the the application is able to take advantage of the wider registers (typically multimedia encoding/decoding, cryptographic, or number crunching applications), you may not see any performance improvement. If you had poor performance before you might not notice any improvement. Typically you only want to use a 64 bit version if your hardware/operating system can only run 64 bit software, or you are exceeding the 4GB virtual memory space limit.
Unofficial 64 bit builds of Firefox, Thunderbird and SeaMonkey for Windows are available at wiki.mozilla-x86-64.com . The Third Party/Unofficial Builds forum has optimized 3rd party builds that may include some 64 bit builds for Windows.
WaterFox and Pale Moon are optimized 64 bit versions of Firefox for Windows. Start64 and Firefox 64 have several 64 bit builds of Firefox (nightly, WaterFox etc.) for several operating systems. Start64 also has 64 bit Thunderbird builds.
Many Linux distros provide their own 64 bit builds of Firefox, Thunderbird, and SeaMonkey in their repositories.
64 bit Daily builds (Thunderbird) are available at http://ftp.mozilla.org/pub/mozilla.org/thunderbird/nightly/latest-comm-central/ . These should be considered experimental and may break for a while if 64 bit specific issues are encountered.
Extensions and themes
Most extensions and themes don't care what operating system you are using, or whether you are using a 32 bit or 64 bit application.
You can not use a 32 bit build of Lightning with a 64 bit build of Thunderbird or SeaMonkey. There are official 64 bit builds of Lightning available for Linux and OS X but they're for nightly builds. Nightly builds are automated untested builds . Unofficial 64bit builds of Lightning for Linux are available at here. Also look in the contrib subdirectory of the latest release in releases.mozilla.org
The Enigmail extension supports Linux x86-64 but doesn't support 64 bit OS X.
You need to use a 64 bit version of a plug-in if you use a 64 bit Firefox build. The Adobe and Foxit web sites auto-detect whether you use 32 or 64 bit.