Are digital games purchased through Microsoft store & saved data linked to my profile?

If you already have the console and have it set as your Home, it should start installing automatically. Otherwise, you can go into your Games and Apps and start the download there.

ok thanks, one last question will the download appear instantly?

Yes. You just need to make sure you're signed into the same account you use on the console when you make the purchase.

Game progress is stored on the cloud and will resync when you play.

okay when i download the game my online character will also be there?

Absolutely! Any and all games you purchase digitally through the Xbox Store, as well as games through Game Pass (if you are subscribed), are yours, meaning you have purchased the license to use them digitally on ANY Xbox. Simply download your profile on
the new Xbox, go to Settings and make the new Xbox your Home Xbox, and you're good to go! All games and add-ons you've purchased from the Xbox Store will be in your Ready To Install section of My Games & Apps. All your save data is in the Cloud so once you
launch a game you have save data in, the game will automatically sync the data from the Cloud to your new Xbox's storage.