Do you have to wear the four-cornered garment and a skull cap to bed? If so, do you have to make a blessing on the cornered garments in the morning?
The Gemara in Menachot 43a says that one is exempt from wearing tzitzit at night because of the passuk in Bamidbar 15:39 which says "and you shall see them." Thus one is not obligated to wear tzitzit at night, although it is permissible to do so.
So why would anyone wear tzitzit at night? As a sort of "protection" from the night, in addition to extra Yorei Shamayim. Wearing the kippah at night is the same. It is not obligation to wear the kippah during sleep. (Is wearing a kippah at all obligatory? Maybe "minhag Yisrael Torah hi.") Again, some people do indeed wear the kippah at night for extra Yorei Shamayim.
I have heard a story (I think it was actually somewhere here on Mi Yodeya) of someone who was in a Yeshivah and would take off his kippah during sleep, to which the Mashgiach said he should keep it on. The student said that the kippah always fell off his head at night and got lost to which the Mashgiach replied "you learned how to not fall out of the bed at night; you will also learn to have the kippah stay on at night"!
As for reciting the bracha over the tzitzit the following morning, the matter is a bit more complicated than a yes or no answer. It is preferable to have one tallit katan for the day and one for the night, that way one could don a tallit in the night before bed (in which a bracha would not be said) and in the morning take them off, put on his daytime tzitzit and recite the bracha on them. If however he only has one tallit katan for night and day, then a bracha is not recited. But if one is married, he does not recite the bracha on the tallit katan anyway, because he says the bracha over the tallit gadol during Shacharit.