They can be painted. But the question is why? They have so many colors, just pick the color you want. You don’t have to repaint ever.
My contractor put mine up when he did work on my house. He used black outdoor screws screwed into brink. I know you’re looking to mount onto wood but brick is what I have. Not sure if those screws came with the shudders or not. It’s been 2 years now in the northeast region and no signs of loosening. Still looks great. Personally I would want them mounted as securely as possible and the screws seem to be doing their job.
You the vinyl screws, you just have to make a hole and feed them through. Buy extra screws!
I don't know for sure if you can get color samples. But, if you order the shutters in the colors close to what you think look right (say 2 of Bordeaux Red and 2 of Burgundy), just keep the correct ones, and return the one's that aren't right for a full refund.
My answer is yes. I've had mine several years now and I'm very pleased with them. Also, they paint very well if primed first.