Spot on. It has to be full duplex for cross band repeat to work, whether the guys who write the manual, marketing literature, or QST review realize it.
That's correct, except that the radio doesn't need to be able to use the mic or speaker while in crossband receive mode, so it is theoretically possible to have a crossband repeat capable radio without being able to make use of the duplex capability otherwise.
I believe this is the operative statement. I haven't tried it in a while (years), but I recall that my Alinco DR-610T mobile rig was not able to receive on 70cm while I was keyed up on 2m for a satellite contact. I remember this because it's frustrating when you can't hear what's going on. Haven't tried V/U satellite mobile since (and that was while parked in my driveway).
The DR-610T is definitely capable of Cross-band Repeat, however.
Greg KO6TH