anything and everything
I can't speak to the grammatical correctness but both of them *feel* equally acceptable to me.
I would probably use the exact word used in those sentences. I wouldn't (at least very often) say, 'anything about ancient Egypt is fascinating' nor would I (very often) say, 'everything to do with planes fascinates him.' Weirdly, I'm not sure why. That said, I would say, 'everything fasinates him about planes,' rather than 'anything.' Honestly though, neither sounds that weird. I doubt many native speakers would see that as an error, if it even is.
They can be interchangeable sometimes, and it should be clear from the context. If the context indicates some kind of choice, then they are mostly the same. If any one of these things (anything) please me, then all of these things (everything) please me.
"Anything and everything" is an idiom that emphasizes complete lack of discrimination. There is no other difference between that and "I can eat anything" and "I can eat everything" if the context is clear that it's about a choice. There is a big difference, however, between "I will eat anything" and "I will eat everything". Unless the context somehow clearly indicates that it's about a choice, these are very different.