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, 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 the application exceeds the 4GB virtual memory space limit.
This updated blog post benchmarks 32 and 64 bit versions of Firefox, including Waterfox (specifically compiled for 64-bit) and concludes that "We should see some performance improvements in the future, but Firefox 64-bit doesn’t appear to give you a faster browsing experience at this time." This Ghacks article compares 32 and 64 bit versions of popular browsers and concludes "Most differences are marginal and not visible to the user. "
64 bit builds for Mac OSX and Linux are available at http://releases.mozilla.org/pub/ . Official 64 bit builds of Firefox for Windows are available on the normal download page starting with version 43.0. There aren't any official 64 bit builds of Thunderbird and SeaMonkey for Windows.   .
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
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.