Best to keep your lumber dry. Wet lumber is more prone to warping. But if it's wet, and you need to use it, then use it wet. It will dry in place. Just stay safe. It's not safe if you are working on wet ground with wet materials with power equipment!!!
For the rest of your building materials, perhaps you can put them on a pallet and cover them with a good quality tarp?
Just apply a good stain after it is built. I would recommend Sikkens stain for siding, reapply every 5 years or so. Pine is a very good wood if protected. Another option would be pressure treated lumber, but I would still stain it for aesthetic reasons.
Depends on your location whether plain pine is fine or not. I'm right on the coast, so pressure treated wood and galvanized hardware are a must if I don't want to have to deal with replacing stuff every other year. The salty air just eats through everything.