Coop & run me advice needed

Aloha! We rescued 3 chicks (about 1 week old) and we’re officially attached. We’re in Hawai’i right against AG land, so since they have no mama hen to teach them 'street smarts,' I want to build a secure coop and run instead of free-ranging. I’m fixing up an old spot hit by the Kona low and figure I have about 3–4 weeks before they need to move in. My rough plan is a level run on the left (facing the door) and nesting on the right-side platforms, but I’m totally new to this and open to better layout or supply ideas.
I really need advice on predator-proofing… do I actually need to bury the mesh to keep the mongooses out? I also need tips for reinforcing gaps in the wood, building a proper roosting bar, and keeping that left-side run dry since the gutter is only on the opposite side. If you have any building tricks for a first-timer, I’d appreciate your kōkua! (Red circled area is where I am thinking the run would go)