Correct on ship assist modules, however you do need at least one point of attack to receive attack bonuses and one point of defense to receive defense bonuses but the attack/defense can be in *any* category and the ship will receive *all* categories of assist.
No on ship repair.
No support given to ships with no attack/defense. Also any ship with attack but no defense will only receive attack assist and ships with defense but no attack will receive only defense assist.
No support without specific "ship assist" modules installed.
AFAIK the AI doesn't care about the military starbase's "Area of Influence (AOI)" only about starbases placed near it's planets.
Ships in orbit on planets within a military starbase's AOI do receive the ship assist bonus if the planet is attacked but there is no way that the starbase itself joins in the planets defense.
Also you need to be careful about the distinction between "ship assist" modules that give a bonus to your ships that are within the military SB's AOI versus modules that give the starbase itself attack and/or defense capability. The former can only be placed on military starbases whereas the later can be placed on *any* starbase.