Adding a ground wire to old 2 wire wiring before extending to grounded wiring.
You are asking about the rules for ground retrofit, which were greatly eased in 2014.  We discuss that here and there on the site.  

To answer your questions, 

You can start the ground any old place.  There's no requirement that the ground parallel the supply conductors.  

Grounds for one circuit can be extended to protect another circuit, provided both circuits come out of the same service panel.  That's only an issue if your house has subpanels.  The only restriction is that the ground wire must be large enough for the circuit all the way home.   So for instance if you are retrofitting a 12 AWG circuit, you can bring it to the water heater and its 10AWG ground wire.  Then you can retrofit a #14 circuit and bring it to the #12.  The reverse is not allowed, a #14 ground wire can't be part of the grounding path for a #12 circuit.  

Order does not matter, do it any which way you can.  Several circuits can share ground:  Remember, grounds never flow current except during a ground fault.  

GFCI protection has absolutely nothing to do with the grounds.  GFCI's don't use ground at all, and have no access to ground.  (Well, GFCI receptacles do, but only to supply the ground pin on the sockets; the GFCI device doesn't even connect to ground.) There shouldn't be any neutral-ground connections on the downline wiring; that would be the very definition of a ground fault. 

That means that GFCI protection and ground retrofits are orthogonal; they have nothing to do with each other and can be done independently of each other.