You got the wrong idea here, if you mirror four 3TB drives then you will have just inder 3TB of storage, not 12TB, but you will have high fault tollerance. What do you really want to do or have when you are done? You could shoot for a RAIDZ1 with the four 3TB drives and get about 8TB storage. I have links to two different RAID calculators in my signature, check them both out.
As for the RAM, 8GB is fine for normal FreeNAS use but you might need to add more RAM to prevent a lot of disk caching form happening.
Yes, you move the hard drives into another motherboard and all your data would remain in tact, that is one of the nice features about FreeNAS and not using a hardware raid. You would also be able to use the same USB flash drive, just plug it in and power on the computer. The only catch migth be to tell the computer what to boot from in the BIOS.