To get the FBA core, load Retroarch, go to Online Updater, then Core Updater and select the core you want to download. At the moment I just use FB Alpha, but I also have the CPS-2 one that I use for CPS-2 games (haven’t checked to see if there are any performance differences).
A DAT file is basically a list of games with the correct individual rom names and checksums for that game. You use a program like Rom Center to scan your roms and it will verify if your collection is correct for the DAT file you select. If there are any issues like incorrect naming, Rom Center will rename it. Problems can arise if you are missing some of the individual roms from within your game zip. Finding the game that is the correct version that you need can be very hit or miss.
That is a really basic description of DAT files. ClrMamePro is another really good program to use to audit your roms, but I found Rom Center easier to use.