You cannot do both DXB and DME from LHR. If you are looking for mileage, try IST instead of DME. Virtually the same mileage.

DFW to LAX should be in domestic first, not coach. Business class tickets get to fly first in the US if there is no business offered (subject to availability, of course).

You can book CX YVR-JFK if you want to but it uses up your one allowed NA transcon so you would have to give up LAX-JFK.