Am I able to record me on 1 track and at the same time her on another and then to balance it all and save it to whatever?
No, you can only record one track at a time on the PS-04. It seems to be intended for the solo artist who wants to be a "one man band" and lay down all the parts one at a time.
As far as saving, each track you record is saved to the memory card as soon as you hit "stop". You can transfer one or more tracks to your computer for editing or mixing. The tracks are recorded in a proprietary format, so they will need to be converted before being useful on your computer. You can do that with a utility you can download from the Zoom web site.
The manual sucks. Well, maybe that's too strong. But it is difficult for most folks who check in here out of frustration. You can use the rig to record a live gig, but it will be a single mono track.
For a beginner's tutorial, click on the link in my signature below (PS-04 Recordings) to see what I wrote, including links to various audio programs and the Zoom Card Manager utility.
Your adventures into care homes is a great thing. I used to play with a guy and that's what we'd do. We also played a couple of restaurant gigs, but in the care facility, we had full attention. Currently, I go into schools and libraries with another musician to play for kids. Quite rewarding.