I can't seem to get them to eat the food regardless of how close/far I get said food to their mouths.
It seems like you have to hold the food item over their face, and wait a little while as they eat it. Letting go too early results in the food being dropped.
Yeah, I was in the same boat as OP and kept buying food only to drop it immediately after. My first girl starved to death as a result :x
I have a feeling there might be some kind of bug related to full-screen mode (or maybe not?)
I'll try to fix it if I can reproduce it. If it doesn't reproduce, I'll give up on fixing it.