it is allowed in daily. For starter there is even analysis board button.
None of live games it is allowed
Ok. I've never used it. I also don't use computer assistance either. I want my rating to be accurate .... not over-inflated. I already have my ego for that. lol
I've scored around 1560. I play above that on chess.com by taking more time on moves than I took on that tedious test, and also using the analysis board to work out lines (which you can't do on that test).
You're not supposed to use an analysis board during chess.com games. I'm pretty sure that's cheating (not sure about daily games). Anyway, it's better to force yourself to look ahead several moves, without using an analysis board. Then you'll be able to play that well in a real, OTB game.
I think it's allowed. And on the contrary, I find I can do board moves in my head better after using the analysis board, I think it's helping.