Not an official answer, but at least one from a lead playtester...
Radiation damage: yes, it's extra damage. It's affected by dampers. Yes, it does SI; this represents systems being blown and welds weakened by induced currents, secondary radiations, etc.
Not having the extra SI is not a big deal. It will make the survivability of larger ships in major combat higher, but one crit can often terminate even the largest cap-ships; most of the playtest was sub 10KTd. We (my group) didn't apply armor vs Radiation; dampers were used instead, not in addition.
A nuke missile doing 5d6 + 1d12 successfully attacks a ship with AR 3.
The rolls are: 5,5,6,1,3 + rad(iation) 6.
SI damage =11 normal + 6 radiation as I understqand the rules. Two internal damage rolls: one normal, one radiation.
Why Radiation? Since heavy armored vessels can often survive big hits, but often have no radiation protection to speak of... and so radiation hits can whack even them. Or, for the purists, it's a hold over from High Guard.
Why no Rads? It was discussed, but we didn't have time nor agreement on how to do it; Hunnter, I think, decided to leave it for later supplements.
x1 Crit: No extra damage, save that armor does not apply. (Nor screens, etc.) Armor and screens not applying is plenty extra damage, though.
Batteries: Yes, one to hit roll per battery to get full damage and bonus. The tighter grouping increases penetration versus armor, improves to hits, and against poorly armored targets, can result in much more damage. For multiple internals, howerver, lower battery values are not a "bad thing" per se. Pirates will want to use the minimum UCP to get past armor; knocking out systems is more important than killing the structure.