This is a really great mod ! But it seems that while you are in the sandbox, you don't have your real-world notifications, like being attacked. Is it possible to have the notifications of our real-world to avoid returning to a ruined base ? Or at least pausing the game while in the sandbox or being attacked ?

Neither of those are possibly, unfortunately. Well, pausing is impossible; there are some rough ideas for working around the alerts, but the short answer to that is that the mod would work pretty differently to allow that to happen.

The mod Game Speed Button allows you to control the speed of the game: https://mods.factorio.com/mod/game-speed-button

Can you either stop completely or slow the time a lot, inspired by the mod, while in the sandbox ? Or slowing down the sandbox will have the effect of stopping the simulation in the sandbox too (belts and inserters) ? If so, maybe just an option to automatically slow the time when entering the sandbox and restore the default time exiting it ? Check the mod, it has a GUI button to control the time and options to select how many speed options it has.

What happened to me is I was in the sandbox for a couple of hours brainstorming some ideas and in my world, the bitters evolved so much that I had to restart my game from scratch, unable to fight them anymore :P

This is simply how the game works, and how this mod is able to work as well. The sandboxes cannot work on a different timeline.