It's your choice whether you have both passes on 1 device or on separate devices. If they're on 1 device though, you can't travel separately.
Each pass has its own trip. The trip is stored on the device and a change to one trip doesn't automatically change the other. If the passes are on the same device, you can add a journey to multiple trips at the same time.
Whether you're logged in or not in the app doesn't make a difference. If you're logged in, then you can see in the app any reservations you made on the Eurail website. That's however the last place to book reservations, because of multiple reasons, one of which is that it's more expensive than elsewhere. Instead, use this page as a guide:
https://www.seat61.com/interrail-and-eurail-reservations.htm
In addition, the app should not be used to plan because it's incomplete, often out of date and generally unreliable. Instead, use national websites or apps; for international travel, www.bahn.de or the DB Navigator app is a good choice.