Should have noted in the OP, directly to the right of this picture is the refrigerator

Are you talking about putting it in the corner?

The dishwasher can go literally anywhere as long as you run power, a water supply, and a drain hose to it. The closer to the sink, the better, because those lines typically connect under the sink, but so long as it will fit where you’re indicating, I don’t see a problem other than losing that cabinet space.

No, where the two open cabinets are. But they are separate boxes. Would knocking out the two outside walls of those two cabinet boxes be problematic?

Should be fine. Might need some support adding. You'll know when you take it out if you need to solve any structural problems.

What's your plan for the drawer? Half drawer?

All standard dishwashers need a 24" space. If the cabinet is a 24" cabinet then yes you can fit it. Wider will work with creative work but less than 24" won't for a standard DW

Most cabinets are boxes screwed to the wall and screwed to each other. And maybe some screws into counter top. As long as you have 24" then yes knock that box out and use a gable against the fridge for support. You need 24" clear is really all you need to know.

I don't know whether they're still available, but when I was a kid we had a portable dishwasher, and I know someone who still uses (an old) one. These roll around the kitchen, have a counter -- or cutting board -- on top, and load from the top. The inlet hose/drain hose attaches to the kitchen faucet with a quick-release connector. The unit plugs in to any wall socket. Saves changing the cabinetry. Gives you a floating island counter.

Be sure you have enough clearance for the dishwasher to open fully. (The cabinet doors on the far right.) Depending on the swing of the fridge you may need to have a little spacer there as well.