Can a missile be fired when a fighter jet is inverted?
The combat advantage of fighters (as opposed to heavier-payload bombers) is their maneuverability, therefore a missile delivery restriction such as g-limit (think Sidewinder heat-seeker in a dogfight) or attitude would unnecessarily restrict their efficacy.

As a Vietnam-era fighter and attack pilot I fired both unguided (aim and shoot rockets) and guided (target lock-on and shoot) missiles, and neither had associated attitude limits. Missiles that fall clear of the weapon station before rocket-motor ignition (such as the TV-guided Walleye or the optically-pilot-guided Bullpup) are obviously restricted from negative g to ensure safe separation from the airplane, i.e., negative g release from an under-wing weapon station would all but guarantee impact with the airplane.