It says that when a solarian is in photon mode you get +1 insight bonus on damage rolls. Since it states just damage rolls in general, does that apply to spaceship combat when firing weapons?
It does not
Unless an ability is said to affect starship/vehicle combat, it does not affect it. This is explained in the Core Rulebook, page 322, under Actions:
Class features and items affect crew actions only if specifically noted in the class feature or action.
The FAQ does list one exception to this rule though:
Does this mean I can't benefit from the skill bonus of operative's edge, or an envoy's skill expertise?*
No. When actions taken in starship combat call for a skill check, any class feature that grants bonuses to or allows rerolls with the relevant skill applies when using that skill as part of starship combat. This is an exception to the rule.