Welcome,
Glad you found the FAQ...
To answer your few questions above:
DAT = Digital Audio Tape, the digital version of your cassette walkman, uses smaller DAT tapes. Preferred, though slowly going extinct, recording device. The most popular are: Sony D7, D8, D100, M1 and the Tascam DA-P1. Lots of other kinds of DATs outh there too.
DSBD vs. SBD = DSBD is a shortened version of SBD>DAT. I have yet to encounter a true digital soundboard at a venue. In a sense, all SBDs are DSBDs, unless they are SBD>analog recorder, in which case, they could be labeled as ASBD, though no one ever does...
Matrix = SBD + AUD
Polar Patterns = Changing the microphone cap on some mics changes the way it records, or rather changes the field from whcih the recording is made. OMNI, as the name sounds, records in all directions. CARDIOID records in front, HYPERs focus in on the front, etc. etc. Some mics require you to change the capsule to change the configuration of the mic. Others have all (or some) built in and all you do is flip a switch. Some mics are only one config (like mine).
If you live near a taper, or are friends with one, I'd ask them first - only because they are available to you faster and more conveniently than here.
But ask us and we'll try to answer!
Terry