Can you buy health insurance without an ARC or visa?

Would some visitor who is just making 90-day visa-waiver stays in Taiwan on a US passport be able to buy Taiwanese health insurance, or is an ARC or visa needed?

Also, are dental and medical insurance separate things, just like in the US?

I have it on very good authority that you need a resident visa to buy health insurance in Taiwan, and you can not buy health insurance if you are only here on a visitor visa.
Most normal dental work can be done on the public health insurance scheme here.

Basic dental health is covered in NHI. That includes extractions and I think root canals. The cosmetic part of the procedure (crowns and implants) are not covered. Crowns are about 10K/tooth while implants are typically about 80K/tooth although you can find both a little cheaper.

And Bernadette is right. No ARC = No NHI.

You can by AIG health insurance for travelers or something similar.