I'm not really going to be writing about feeding zombies--we don't eat. Although some people speculate that we "feed" off of ultraviolet radiation, and others think that we actually absorb moisture and toxins from the air, sort of like undead air filters. I've got a friend who is testing the UV theory, using one of those lights that people use to grow plants.
But in terms of "caring"--I've had some discussions with folks at the Haunted House about a number of topics regarding zombie/trad relations, the difficulties and barriers that exist. One of the first--and biggest of these barriers is the difficulty most zombies have with expression. Our post death-bodies, for whatever reason, don't lend themselves well to expression, so if you have an undead friend, you are unlikely to be greeted with the smiles, lightening and softening of the eyes, and rosy-cheeked expressions you get from your trad friends, unless that undead person is trying really, really hard to be expressive. And we are well aware that the results of our attempts at expression are sometimes, well, grisly. Picture an eyebrow frozen in a permanent arch, a smile that reaches only one side of the face and shows too many teeth, an eye made permanently lazy. Most children learn expressiveness from their parents beaming down at them in their cribs; all of that needs to be re-learned, and the unwilling muscles retrained after death.
Undead people are frequently frustrated by the attempt to show expression. Karen, who is particularly good and "natural" at it, actually works pretty hard at making her facial expressions seem effortless, but for other kids it can take months.
Positive feedback, works. Saying something like, "Hey, Kev! You've been working on your smile, haven't you? Looks great!" can go a long way towards making a dead kid feel good about the effort they are making, whereas framing your comments in a negative manner, like "Yo, Sylvia, only half of your lip is working" is a guaranteed buzzkill. Never, never, never suggest to an undead person that they "turn that frown upside down". We can't be held responsible for the consequences.
And for zombies, I'd suggest that you stay patient with your trad friends who might be having a difficult time understanding you. A great deal of communication between people is exchanged non verbally; living people send out hundreds of different signals and cues from posture, expression, gesture, etc., so it can be very difficult trying to "decode" a person who doesn't exhibit any of those behaviors. Think of how easy it is to send mixed signals to people, even ones you know really well. Think of all the times you accidentally hurt someone's feelings when you were trying to do the opposite.
The key, for both living and dead, is patience. Ask questions, communicate often, don't be afraid. I think everyone will find it is well worth the effort.