No. It is way too far. You can walk from Port Orleans, Riverside to Port Orleans French Quarter, and that is a bit of a hike. However, my grandson and I made the walk, so that he would swim in the French Quarter Pool, with the dragon slide.
People just don't realize how big WDW really is, until they visit. You are definitely at the mercy of their transportation system, unless of course you drive your own car, and/or rent a car.
Yeah.... No you can't. It's too far. No walking trail. Either take the bus or the water taxi.
FYI, the water taxi will still run when it's raining but yes, if there is lightning within a 5 mile radius, it'll get shut down and the bus will be your only option (or a taxi if you want to spring for it).
Honestly I wouldn't bother walking resort to resort or resort to park. It's so massive it's literally ridiculous. I'm a bit of a hiker and I bet you it would take you a few hours to pull off walking anywhere, even if you are ambitious, I wouldn't even feel safe. The roads are highways and the walking trails are full of all kinds of wild southern animals and reptiles that I personally am not accustomed to or feel safe being around.