yes they can
Your could scrub the scabs with MTG, and keep a light weight water proof turn out sheet on her to stop the moisture which is why rain rot develops.
If it isn't itchy or painful to the horse, it could be ringworm.
it can do, yes. laquer it first to avoid it.
Yes, any wood that is exposed to rain water can rot, to help prevent rotting, the wood can be coated with a waterproofing agent, such as Thompson's waterseal, or a waterproof paint.