You might not know this but Mozilla plans to switch 32-bit users who meet their system requirements* to 64-bit builds of Firefox in the coming future.

* Win7 SP1 and above, 2GB+ RAM

Yes, you can use 64-bit builds of Firefox with 4GB of RAM. I usually say 4GB is the bare minimum to have when using 64-bit Fx. It does use a tiny bit more memory but the speed more than makes up for a few hundred MBs extra.

Edit: Apparently as of today's Fx55 release, Win64 users will automatically get the 64-bit version if they meet the requirements listed above.

Note that you currently have the 64-bit Firefox 55 version (Win64 official WOW64 for 32-bit).

• Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:55.0) Gecko/20100101

See also "Help -> About Firefox"

I think you're right, that 64-bit programs use somewhat more memory. I don't know whether it makes a difference in the real world.