I'm honestly not sure about the mattress protector, I think you would need to be able to see it in the flesh. Someone on here has said they use a polyester one with no bother but I had read that it needed to be cotton so have 100% cotton ones. The crucial thing for me with that one though is if you scroll down there is a picture of a cup of water spilled and the water sitting on top. It may be that there is some sort of coating on it and that if you flip it over the other side would absorb but without trying it it's hard to know. With mine I fell foul of this as I didn't realise there was a "right and wrong" side and the wee definitely just sat on top when i had it wrong way up with the repellent side up. I had a bit of a job finding 100% cotton but did find two in Homebrands (the TKMaxx home store) after going through a big pile of about 20 unsuitable ones. I paid about £18 for a kingsize one which was big enough for two 2x4 size with some spare for piddle pads.
Fleece looks right though.
Yeah, they are both 100% cotton right through. I haven't noticed it feeling particularly heavy when wet though, once it has been washed and spun it is ok. It did feel like a leap of faith cutting into it I will confess that! When I cut into it though it was quite fluffy inside, a bit like the kind of wadding/batting you buy if you are handmaking a quilt.
Yes, it works great as a protector. I did manage to shrink both of mine after making them though so they don't fit as well as they should now, but that was my fault for not allowing for shrinkage because I had prewashed. I tumbled one of them (not sure what I did with the second) so the workman at fault rather than the tools.