Definitely caulk. You never want to give water any chances to get into your walls or flooring, etc. It does nasty things in dark, enclosed places.
I had to look up batten siding. And looking at those pics made me appreciate my t-111 siding a little more. I use a very fluffy roller to help get into the nooks and crannies. But if I really wanted to spray, I think I would invest in a large tarp and tape off the wall of the house and spray away.
I am not sure about your other questions. I know I would need help with those projects.