If any United States political party asks for your support,do you have the right to fully question everything about that political party ?
Absolutely. Never give your support to anything in life without first knowing the facts.
Most of your questions can be answered in their websites. Some will require detailed questions of candidates. But yes, to support a party you should understand as much as you need to know about that party in order to make an informed decision.
Its a duty .. not a right
Sure. They may not tell you but you have the right to ask and the right to refuse to donate.
Absolutely. The framers, or founding fathers set up our system and gave us the constitutional right(s) to question, peacefully protest and peacefully speak out against government and politicians.