Wouldnt we be able to buy a short propane hose and connect to burner and nr heater regulator?
Might be able to do that, if you can first disconnect the brass fitting from the original hose, the part with the orifice that meets up with the burner tube.
Is the hose connection to the burner tube unique?
Yes it's my belief that it is. Or at least, "not common" in the sense that many grill hoses just have a threaded part on the end. Ours don't. The brass end on our clips into the burner tube.
... is the new touch n go regilator hoses one piece units hard fixed to the regulators
Excellent question. Don't have the answer to that. Never seen that piece in person.
Dunno if you've looked at yours yet, so I don't know if any of this makes sense for you. I wouldn't be concerned about the appearance of the regulator or the bracket. It either works well or it doesn't.
The good news is that the hose is reliable unless damaged. The regulator is cheap and easily swapped out, as is a modern ACME nut for quickly attaching/detaching the tank.
Get a tank connected, even if it's just a borrowed 20lb from someone's gasser and see what happens. Leaks will either be heard by ear, felt by hand or seen by soapy water. Not much mystery there.