1) AFAIK the 767 fuse is produced in Spirit and then has to be transported to Everett, where the co-located 748F & 767 lines seem to be running-out of space;
As noted, the nose and tail sections are made in the US with the center fuselage (main cabin) are made in Japan. The wings and horizontal stabilizers are also made in the US with the vertical stabilizer made in Italy.
As for the FAL, Building 40-33 handles the wing letdowns as well as joining them together (there are spaces for between three and six sets). There is also room for two vertical stabilizers and two sets of horizontal stabilizers. The FAL itself is located in Building 40-32 with two stations (Final Body Join and Functional Test). To either side are multiple fuselage assembly jigs allowing two for each section along with one for a complete forward and aft section.
2) It surprises me that BA has such a huge supplier of critical parts with no cross-shareholding (EG no second-source exists like say the (3or4) Engine OEMs)
To be fair, Airbus does not have multiple suppliers for each fuselage or wing section for their airplanes, either. I'm guessing the suppliers they have are capable enough of meeting the demand.
3) Certain commentators regard an amalgamation of all 787 production at Charleston as a certainty, in part to erase the "Dreamlifter" task;
The Dreamlifters would still be required to fly the wings and Section 43 from Japan, as well as Section 41 from Wichita and the tailplane from Washington and Italy.
4) Why not also transfer a quantum of 767F/KC-46(?) production to Wichita for the same reasons, thus also freeing-up space in Everett?
Wichita would need to have a complete FAL built there and I am not sure how the logistics of the parts deliveries from Japan and Italy would need to change to accommodate production there as opposed to Everett.