Cannot log into windows on One Note or Xbox Game Pass on PC.

The Xbox app should already be installed on your PC if you have Windows 11, otherwise you can use the Microsoft Store to download the app on Windows 10. Apart from that, yes, you log in with the account that has Game Pass Ultimate. You should then be able to play two different games at the same time using the PC and the Xbox.

On another note, if the one on the PC is trying to play the games using the cloud, that will be why the other one on the Xbox gets logged out. The one on PC should just install the game on the PC and launch the game on there.

The link Jesse gave you is for the XBox version, this one is for XBox Game Pass on PC:

Fallout 1st (Windows) — Fallout 1st (Windows) – One-Month Membership | Xbox

Note the (Windows), that's the difference.

Unfortunately Game Pass is not available for the 360. You would only be able to use Game Pass on the PC or Xbox One.

Xbox Game Pass Ultimate:

Use your active Xbox Game Pass Ultimate membership to play games on Xbox One and Windows 10 PC (excludes Windows 10 in S mode). Xbox Game Pass Ultimate includes Xbox Game Pass for Console, Xbox Game Pass for PC, Xbox Live Gold and additional benefits. Note:
Purchase of Xbox Game Pass Ultimate automatically upgrades your existing Xbox Live Gold or Xbox Game Pass membership(s) to Xbox Game Pass Ultimate at a conversion ratio each based on days remaining. Learn how this works at www.xbox.com/gamepass. Future code
redemptions are also subject to a conversion ratio. Conversion ratio subject to change. All conversions to Xbox Game Pass Ultimate are final: Once converted, you cannot re-convert your Xbox Game Pass Ultimate membership back to a previous membership. Maximum
36 months of redeemed Xbox Game Pass Ultimate per account at a time, including any converted time from Xbox Live Gold and/or Xbox Game Pass (for PC or console).

Yes, and no. While you cannot be logged into two of the same Live enabled devices at the same time , you can be signed into cross platform LIVE enabled devices simultaneously.

When I say "Live enabled devices", I mean Xbox One; Xbox 360; Windows Phone, Windows 8; Games for Windows - Live (note that GFWL cannot be singed in at the same time as Xbox 360, logging into one will sign you out of the other).

You might also wish to note that this thread is nearly a year old, so you probably should have simply started your own thread.

She can play any of the Game Pass for PC games on the PC. It does not matter what games she downloads to the Xbox One. As long as she has Game Pass Ultimate she only needs to log into the Xbox App on Windows 10 to download and play the games. As long
as the PC being used has the hardware capable of playing the games.