I want to purchase digital game from Microsoft store but uncertain if it will install on...

The game should install on your Xbox One if it is set to instant on. If it is set to power saving mode, then it should install the moment you switch the console on.

If the games you want back are Hardcopies then no Microsoft would not replaces those, if they were purchased digitally from the Xbox Store then they would appear in your games to install list.

If you bought it from the Microsoft Store then you purchased it digitally so it was automatically added to your account. You would just install it from the store.

Did you purchase it digitally or on disc? As long as you purchased it digitally, you should see the game listed as ready to install in your library in the Microsoft Store app.

You don't need to install anything to have gamepass. Once you purchase it, it is automatically put on your account. If you want to play games on the PC, goto the Microsoft Store, and find the game that is on game pass, then select install from the game
store page. If you want to install the Xbox beta app, then just install that from the store as well.