1. Nope. If you want to stay far away from Maho Beach, you'll want to rent a car. Taking taxis all the time is not worth it, and you'll feel confined to your hotel. It's not really possible to walk many places. Car rental is cheap; almost always cheaper than taking taxis even on one round trip per day from one side of the island to the other.
2. It's relatively safe, but I wouldn't wander around without knowing where you're going. Generally the tourist areas are safe. But I don't think it's a good idea to walk around randomly until you know the island better.
3. I'm from NYC so my scale might be a little skewed, but I don't find it all that expensive to eat there. Regular lunch/dinner prices are about what I'm used to. About $15-$20 per person. Less if you go to a "Lolo", which are locally owned, locally operated restaurants. But - and I say this not knowing how much has been repaired after the hurricane - I would at least set aside one night for some of the really high-end French food you can get in Grand Case. When I was there last, a few months after the hurricane, that town had been completely destroyed. But I did see some of the restaurant owners working on repairs even then, so maybe it's back in business now. If it is, that is some of the best food you will *ever* eat. You can probably also find good food in Marigot, which probably withstood the hurricane better, but Grand Case was/is where all the best places on the island are.
The most common currency on the Dutch side is US dollars. On the French side, they seem to prefer Euros. But on either side, they usually will take either one, and will just calculate the equivalent price for you in whatever you have. You might come across one or two places that won't do that, so it's not a bad idea to ask to make sure, especially on the French side. Of course most places also take credit cards.
I'd recommend trying to look up how much of the island has been repaired before deciding where to stay. I have stayed in Oyster Pond several times but last time I was there, almost nothing was left. The Maho Beach area I know is mostly back to normal. But I'm not sure about the rest of the island.
I'm tired of being a wanna-be league bowler. I wanna be a league bowler!