As far as I know yes you do
No automatic entry into lounge on domestic flights. But if you have a United Club VISA card ($450/year), you have anytime (when flying United) access.
No, first class does not give club access. You may purchase a one time pass. I think it's $50 a piece.
I think you have to purchase the United lounge pass; it costs $54 per person now, I guess. As I have a credit card with them, they send me two per year as a gift
Yes
Thanks! Your answer is awaiting moderation.