Wealthier Egyptians (such as the Pharaoh) had beds, although we would probably think of them as cots. They were wooden frames with leather or linen stretched across them. Egyptians generally didn't use pillows, as far as we know, but had headrests made of a variety of hard materials. By the accounts I've read, these are actually quite comfortable provided you sleep on your back.

Interestingly, some Egyptian beds were actually slanted, with the sleeper prevented from sliding off by means of a large footboard. I've never heard any confirmed explanation of this, so that's yet another cultural artifact lost to time.

(Note: given that pillows are generally made of material that decays quite easily, it is entirely possible they've simply all been lost to time. Some debate surrounds whether or not the Egyptians used cushions on their headrests.)

They certainly had blankets. It gets COLD in the desert at night. People in ancient Egypt generally seem to have slept on the roof of their home, rather than inside it, although the very wealthy my have had proper bedrooms. The well off used linen bedsheets. The poor...well, I've never come across anything saying what the poor used. Presumably rougher linen or woven reeds or something along those lines.

I'm afraid I've never encountered anything regarding Egyptian bedclothes. Sleep seems to have been a bit of a touchy subject with the ancient Egyptians, being rather akin to death, which was something they didn't even like to refer to directly. Our sources from pre-New Kingdom Egypt are already limited, so you can imagine how little has survived on 'taboo' subjects. There are not, to my knowledge, any detailed images of people sleeping from pre-Roman Egypt.