The national guard is part of the military, so funded and supported by the feds. Unlike normal army units though, each state or territory has its own national guard unit under the command of the governor. The intention is to give each state the power to quickly respond to emergency situations without needing federal approval. They’re the successors to the old state militias, but have much stronger federal ties now.
Not even close. Any spot on the Maine coast should be within an 8 hour drive. The populated areas should only be a couple hours. Florida is like 30 hours of straight driving from Vermont