Yes, for daily games. Not in live games though.
Can we use the database?

I don't have clear for how long is ok to use a database. It could happen that both players memorized the same game and are just reproducing it for lots of moves, far beyond the opening. And I believe that is excessive use of the explorer. I'm wishing for a written rule on this. It's likely the case that it exists and I haven't seen it yet.
I use a paper book for the openings, and I was thinking to adopt that at most 10 moves is what I consider the opening and the usage of the book.

I don't have clear for how long is ok to use a database. It could happen that both players memorized the same game and are just reproducing it for lots of moves, far beyond the opening. And I believe that is excessive use of the explorer. I'm wishing for a written rule on this. It's likely the case that it exists and I haven't seen it yet.
I use a paper book for the openings, and I was thinking to adopt that at most 10 moves is what I consider the opening and the usage of the book.
You can use the database until it runs out.
What do I need to know about Fair Play on Chess.com? - Chess.com Member Support and FAQs

ok. Then what is a tablebase? I see that in the fair play post
Ok I'm sure someone here will correct me if I'm wrong -- but I'm pretty sure this is correct: Tablebases refer to "solved" >endgame< positions. It's my understanding referring to these references is >not< allowed in any rated play on the site.
What is allowed is using the "opening move database" (but no engine). For daily games only, not for 'live' games.

Correct. Table bases are solved endgame positions to mate. So one gets 7 piece tablebases that start when one has seven or less pieces on the board (combined black and white pieces). As one makes a move in the table based board it will tell one immediately who has the advantage and which side will win and in how many moves. Consider it a magic "see into the future Chrystal ball" lol. But seriously...essentially the table base is a massive massive database of every conceivable move when there are 7 or less pieces on the board. One does get smaller table bases e.g. 6 and 5 pieces as well. It's a very handy tool to use for studying end game tactics. However one is NOT allowed to use it in live and daily/correspondence games. Considered cheating.
As others have said...it is totally legal to use and read up on opening theory while playing a daily game. You can also use the opening database on chess.com too. Now there is the possibility that you will find a past game in the database that matches your current daily game moves exactly. So conceivably one could play well past 10 ply if both players decide to "copy" the game in the database. However that's quite boring 😴. Plus you won't be playing your own game...and what's the point in that! I generally learn openings 10 moves deep in general and then continue using my own brain.
I see daily games as the learning arena where one has the chance to reflect and analyse and memorize, which prepares one for otb and live play.
Can we use the database or explorer?
I know that we cannot use engine