It's totally safe to open another game using Guide, without exiting current one first?

Yes it's perfectly safe. You can exit from the game or from pressing the guide button and pressing y.

Hi there,

are you talking about a specific game, and what exactly happens when it's counting time?

If this is on a Xbox One console, then you can try Exiting the game via the Guide or setting the console to Energy Safe mode, which will result the console fully shuts down.

Dear, I invite you to factory reset your console.

Press the Xbox button to open the guide.
Select Profile & system > Settings > System > Console information.
Select Reset console.
On the screen

Reset the console? you will see three options1:

Reset and remove everything: This option resets the console to factory settings. All user data, including accounts, saved games, settings, and primary Xbox associations, as well as all games and apps, will be deleted1.

Reset and keep my games and apps:

Use this option as your primary choice for troubleshooting. Reset the OS and remove all potentially corrupted data without deleting your apps or games

Cancel:

To exit this screen, simply select the Cancel button. Up to this point no action has been taken. This is a safe way to exit this screen

Hey, oOUTSIDERo62! That email is one of ours, and is totally safe to take. You are free to take that survey without worrying about your account being taken. :3 Thanks for double checking with us!

It's totally safe, however, check to be sure it's safe with the mother first haha.