In my deck I use two Time to Feeds. I understand most of the rules about Fight, but I am unclear on cards that would prevent damage dealt in a turn. For example, if I make one of my creatures fight one of my opponent's creatures, then my opponent casts awe strike or a similar card that prevents damage (not combat damage, like fog, but just "damage"), does that negate the fight? Did I just waste my fight card? I understand (I think) that Fight is NOT combat, but is it still considered damage?

If you read the reminder text on Time to Feed, you'll see that "Each creature Deals Damage equal to its power..."

So yes, it is damage, it just isn't combat damage. Think of it as damage from a burn spell or an ability (lightning strike / boros reckoner).

If a card negates damage from a creature, the fight damage will be prevented because you are making the creature deal damage.