I dont see a page with the rules for Online-Chess. Many people seems to handle onlinechess different. What is allowed, what not. Can i use opening explorers other then the one at chess.com, books, opening books for chess-computers as fritz opening book or Gen18, game collections including computer games,... ? May i use megabase and search for positions?

A webpage with these rules would be helpful

Here's the link: What are the rules for playing?

site-playing-rules-a-guide-for-the-perplexed.

My grandson and I (very different ratings) would like to play online chess from the same computer with different names of course. Is this considered cheating as it is in other online chess sites?

That's not a problem at all. You might enjoy the option of playing an unrated takeback game for coaching purposes, but a rated game is also fine :)