To add to lizzzi's comments.
Re driving - if you're in the US, each state has a process to evaluate if someone's no longer safe to drive. You can likely make a report and have the DMV/Secretary of State/whomever look into it. If the license is taken away, then driving is off the table. If they continue driving, they can be arrested. However, the process may or may not keep you anonymous. And it's the government. It can be a pain. But research it.
Caregivers are well known to have poorer health outcomes, etc BECAUSE they're not taking care of yourself. Don't let that happen to you. Take care of yourself - physically, mentally, emotionally. This is not entitled, or spoiled. This is basic you-need-to-be-ok.
Re the emergency trips to put out fires - what would happen if you didn't? Or delayed the trip? Seriously, what would happen?
They fell - you call local emergency services, they get taken to the hospital for treatment and you talk to doctors on the phone. Then you request a social worker. Suddenly, you've got local help, and if they get the doctor to say that they can't go home, suddenly the underlying problem is being addressed.
Car broke - well, should they be driving to begin with? Sorry, but I suspect a LOT of 70+ year olds should not be driving, regardless of what they think. So you give them the phone number for the cab. Let them deal with the consequences.
House problem? think this through - put the consequences back on them, not you.
There's a lot that you can do with a phone call. And if they're embarrassed having an ambulance come get them when they've fallen instead of you taking them to the doctor - your response is "sorry, but if you insist on living alone, this is the consequence." Maybe they'll figure out on their own that they need to move and at least be less resistant.
Calling you constantly? Have a conversation that you know they're lonely, and if they were willing to consider moving you could help them get somewhere that they could have a social life. Then tell them that if they call you during the work day, it needs to be an emergency. When they call you at work, answer AS IF THERE IS AN EMERGENCY. When it's not an emergency, abruptly change your tone, tell them that you need them to call only if it's an emergency and hang up. (note - if you're dealing with mental illness, personality disorders, etc this may not work since those issues may get in the way)
This is going to seem cruel. Because what you're doing is pushing the consequences of their decisions, or lack of decisions, back where they belong - on them. You want them to get a figurative slap in the face so they admit that the current situation isn't working. Yes, you're still going to get involved, but you can decrease the burden in the meantime.
Now, this isn't the best way to explain this concept. But you get the idea. Stop running yourself ragged fixing a problem caused by your stubborn, fearful parent. Let them deal with the consequences of their choices (within reason of course, if it's really bad then yes you'll need to step in, but a lot of what you're dealing with is probably not life or death). Tell them that you'll be happy to help them find somewhere to move, etc. Have empathy for them. But let them face the consequences.