i wouldnt add them as they would foul your water without anything to feed on them. as for how long they last, theyre should be an expiration date on the bottles, honestly i feel they all expire before the date mentioned so keep that in mind. small food = coral food.
theres alot of different coral foods and different corals will require different sized morsels. i fed my scolymia silversides from time to time, which is like a minow or small fish, my acans would take brine shrimp or food of that size and other corals would get coral frenzy (which is a fine powder) just as an example.
some corals respond well to feedings, some will die without them, some dont need any at all for survival.
just for the record of anyone reading along with this, corals dont photosynthesize, they have a symbiotic relationship with an algae ( zooxanthellae ) is photosynthetic inside the coral which they then eat.