1. Change isn't difficult except for taxis sometimes. Bills over $20 are a hassle. Major groceries accept them but they jot down your passport and other info and need a supervisor's approval. No need to pursue new bills.
2. Yes, US coins are freely in circulation; Panama's coins are size/weight duplicates. I've never seen a pay toilet here.
3. By a SIM card at any mall, grocery, or minimart, they're ubiquitous.
4. Not sure, but if there's a way to scam you into paying more, you can be sure they'll try. Ubers and the airport taxi into downtown definitely do.
5. Not very likely. Will probably understand gringo accented tourist locations and main areas.
6. No problem walking up to tourist sites and activities.
7. No beaches in the city. The ones 90 minutes west are inferior, stick to your plan.
8. No problem at all, all pax disembark to the main terminal, you can do as you please until you decide to go downstairs and through immigration / customs.
9. I can't opine on El Panama's party specifically, but the hotel is usually a happening place, and you're well located if you go somewhere else. I've never been aware of any "go-to place" for NYE.