Whether to do a passthrough, half-wall, or full wall all depends on how you want the two rooms to feel and function (both separately and together). So, I cannot tell you what will work best. However, my brother recently renovated his kitchen (nearly finished) and changed a full wall to a half wall between his kitchen and dining room. He tends towards more informal gatherings and he wanted to help the small closed-off kitchen feel larger and more open to the house. He does not like upper cabinets and with the remodel was able to acquire additional lower cabinets to make up for the lost storage. He has no stools on the dining room side of the half wall, though the granite does cover the top of the half wall. (In fact, the dining room is simply too narrow to accommodate a table and chairs and counter seating.) His new kitchen feels very open and light (the dining room is on a corner and light floods in from two large windows) and he is extremely happy with the result. Your inspiration picture is very lovely. The detailing on the window is beautiful and could probably be duplicated through wood trim on a pass-through if you would be interested.

The doubled up joists "every 6 feet" could be a couple things. There could be a cantilever upstairs and that could be the first and last joist of the overhang. It could be a headset for some havoc or plumbing. It could be that there is a load above it that needs transfers below. Could have a load bearing wall above it. Either way, it should not have any effect on what you seem to be trying to accomplish here.

yes, remove the threshold molding piece, and lace in the new w/the old. if some of the older pieces can be removed, put the newer ones in that place and the older ones w/some of the newer ones. (Unless, can the older floor be refinished? prob not) in any case, once the island is done it should look ok to the eye. you could always throw down a runner. the other option would be to use a slate or porcelain tile floor in the kitchen area

Sorry but we need an actual to scale drawing to give any advice . Use graph paper make sure all windows and doorways are clearly matked where those doorways lead all measurements clearly marked and the drawing able to be enlarged . If the kitchen is 11 ft wide you do not have space for an island . That is why we need to scale drwaings , you can make anything fit on a piece of paper with no parameters/