Maybe I'm not thinking through this enough but what does this lowered ceiling need to really support? It's not replacing the flooring system. It's not structural. It's just to hang some sheetrock on, right? I don't know how much you need to really worry about joist hangers and weight, even with the span you are talking about. I would likely just frame it like a soffit, a really large soffit, and call it a day. Granted I know nothing of code and I'm not sure I understand the whole support issue you seem to think you have. Are you moving walls or changing anything structural? Or are you literally just creating a lowered ceiling of sheetrock?

I'm not sure of exactly where you plan on putting the additional cabinets. If it's on that wall across from the DW and next to the door, you won't have clearance for traffic at all. For the fridge, the cabinet that is over the fridge looks to be a 36" or 39" cabinet, which is appropriate for a 36" (standard) sized fridge. Your fridge looks to be a 30" sized one, and this would leave you (and any future owners) without the option of getting a standard sized fridge in that location. Are you sure you want to imprison yourself to that small a size fridge forever? And, to get a deep cabinet and (very) small broom closet there, you'd need to increase the soffit depth, and go right up to the molding on the door frame. That would leave you with about a 6" exterior sized broom closet (with interior dimensions of about4 1/2" if you chose FRAMELESS cabinets only), because you would need a bit of spacer between it and the fridge. That would be a LOT of money spent on very little gain of usable space. Please post an overhead scale schematic so that we can look at the total layout of the kitchen and indicate exactly where you are talking about putting the desk area. This will help others to help you and also help you to visualize the changes you are proposing and the consequences.

Original white cabinetry here from 1991 when we bought in '98. Like you, we didn't want the trash compactor, though still working. Used it for a recycle bin till deciding we'd prefer a stack of drawers. These cabinets have the manufacturer's name etched inside each drawer. We were able to buy identical cabinets in the same finish in 2002 to fill the gap where the compactor stood. Checking their site just now, they still appear to be making them. If you know the maker of your cabinets, start with them. The new cabinet's white finish was slightly brighter than those that aged in place, but within a few months the difference evened out on its own & became imperceptible.

Adding bar stools in the pool is feasible. If a contractor is SUPER NEAT and protects the existing plaster during this process, you may not need to re-plaster. You could tile the bar stools for an easier "blend" into the existing plaster. Trying to plaster them the same color as the pool may not have the same color results. Besides, it makes the bar stools very noticeable for safety and provides a nice accent contrast. As far as the work planned adjacent to the pool is concerned, your best course of action is to hire a structural engineer to see if it's possible. One who has experience with swimming pools. If the pool is new, the building department would and should have a structural detail of the pool to show particulars such as wall thickness and re-bar used, etc.. Based on an engineer's advice, you can move forward on pricing the job to see if it fits your budget.