Do kittens like to play all day?
No, cats love grooming, hunting, sleeping, just sitting and being cuddled. They like human beings get tired and do not have the energy to play all day. You can find more information on cats at http://www.cathealth.com/NBehav.htm.
Play, sleep, eat and poop. That's it.
No, they need time to sleep. Baby animals usually spend most of their time eating and sleeping.
I have a bombay. Hes about 4 months old and is extremly naucturnal. He sleeps most of the day, and is constantly waking me up by attacking me in my sleep!! They will calm down in a few months.