1) I don't see where Luna claims the frame is their own design. I recall when their X-1 came out, Luna was very clear the frame wasn't their own design. When I was picking up my Apollo at Luna, someone else was picking up their X-1. He asked them what the differences were and the first thing out of the Luna employee's mouth was the frame and where the bikes were assembled - even before talking about Ultra vs M600 motors.
That said, the FLX's website video does claim they designed the frame for the Blade 2.0.
2) The frames look different enough to me that they are probably not made by the same company. Design copying is rampant in China, still. It could be that the same company makes two different versions for the two different motors, and in that process varies some of the other aspects as well, but that doesn't seem likely. Take a close look at the rear and you'll see two different solutions to the rear-entry/split frame design necessitated by the belt drive. That's the kind of detail I don't think they'd change just to support different motors.
3) With the Luna being a true fat tire (4" wide) hardtail, I don't feel it's designed for urban mobility purposes. Sure, people will use it that way, but that's not the design intent.
FLX is taking a different approach with the Blade 2.0, even including a "Touring" configuration with comfort seat, suspension seatpost, racks, fenders, lights, etc. Its tire size is 27.5x2.6" .