How to secure shoe moulding against metal frame
The only option is to nail it to the floor. If you attach it to the door frame, it will be too flimsy.

You could try an epoxy sealant, but water will get in anyway. Preventing water ingress requires a structure that is designed for it.

I wouldn't worry about condensation. Normally, its only when you have a steady flow of water that there is a problem.

Caulk will not do anything. Sometimes at the marina I see funny boats where the owner thinks they can keep out water with caulk. They get a leaky window because they have a sucky boat, so they get the idea in their head that all they have to do is seal the window with caulk. The leak continues. So, they reason they need to use more caulk. You can guess where this is headed. Soon, the boat looks like it should be renamed "Count Caulkula".