Router vs AP mode

I don't think there's a single answer here; it really depends on your preferences. You need a router on your network, and, ideally, any other routing-capable devices running in AP/bridge mode. So, if you think the ISP-provided modem/router has better features, use that as the router, and put the Orbi in AP mode. As others have said, if you want to use the Armor or Circle features on the Orbi, that requires using the Orbi in router mode, and the modem/router in bridge mode. Same if you want to be able to use the Orbi app for management.

The LAN ports on the Orbi router and satellite should work regardless, in both router and AP mode. There used to be an issue with the satellite attempting to establish a backhaul connection over ethernet when it powers on if there were any devices plugged into a satllite LAN port. I think that's been resolved, but I'm not sure. if you want to use the Orbi in AP mode, you could always try putting it in AP mode, and disconnect all the ethernet cables from the LAN ports until the router and satellite are fully booted up and synced. Then, once they're stable, connect any wired devices you want. You could also update to the latest firmware (2.3.1.44) and see if that resolves the LAN-ports-not-working-in-AP-mode issue you previously experienced.