Welcome to Subeta! Games are more for entertainment purposes, and aren't the most efficient way of earning sP. Quests are where it's at! :) As for feeding, you can pop your pets in the resort and the feeding is taken care of for you (unless you're after the Gourmand achievement -- in which case, you have to feed 'em the old-fashioned way).

Not beyond collecting! They're just around during survival for the memorial -- thought there are a lot of tiers to that achievement.