I'm very surprised at rot in teak, it's prized exactly because it doesn't rot. My C34 1988 has teak all over the exterior and in the Pacific NW area is often wet. I surmise that your problem isn't with solid teak rather with plywood, perhaps teak veneer faced.
As to structure, I believe the boat is not structurally dependent on any of the bulkheads or interior furniture. However, I agree, it's somewhat purturbing to have woodwork fall apart.
I've had to replace the counter in the head due to a leak from the genoa track. It's a relatively simple if time consuming task due to the problem of getting the bits cut to shape and into place. The teak from trim came of the rotted plywood without having to remove the plugs and screws. I reused those trim pieces with the new counter top.
Likely, you'll be able to do the same, that is save the solid team parts and simply replace the plywood. Any good specialist lumber supplier will be able to sell you the teak faced plywood. The remnants of the old will give you a template for the new piece.
My guess is that if the bulkhead forward of the galley is rotted you'll also have to redo the galley counter. See tech-notes and projects for information on how to remove the galley counter - it has screws inserted from the underside.