Depends on how old it is, but still - yes. Try hand feeding it canned catfood, or if it's really young use an eyedropper and baby formula. If neither of these work, take it to the vet, and quickly.
Just like young children, a kitten's young years are formative in that their future health and well-being depends on good nutrition and appropriate care. Check with your vet about concerns.
If it is only for a day, don't worry, but if it's longer your kitten might have a health problem. If you continue to offer your kitten its favorite foods and it still refuses to eat, check with your vet.
Yes. Try changing brands of food or getting kitten-specific food for your new little one. Also, make sure he is getting enough nutrition; perhaps you can give him some vitamins as well.