Let's not over complicate this.
If departing on any *A carrier, you will have access to *A business class lounges at that airport. It is that simple. Please read https://www.staralliance.com/en/lounge-access-policy, it is clearly written.

As for the use if the UC member card, both the physical (which the lounge may require) and the virtual app card have a *A lounge access logo.

Bags benefits are specifically limited to checkin with UA.
https://www.united.com/ual/en/us/fly.../chasebag.html
Sometimes it is best to read the online policies.