1) PEX is used widely and 1/2" is pretty standard. You'll need some sort of adapter to go from 3/8 to 1/2. Doesn't the sink have a threaded connection?
As has been mentioned, there are specific clamps and fittings to use. Lowes and Home Depot both sell the products. You can see what they have.
You can use flexible sink connector hoses, something like this:
2) Suggest a RV outdoor shower connection.
3) Blow out with compressed air or winterize with RV antifreeze. Most here blow out with compressed air and there are fittings designed to do this. See this or use a quick connect version: