Need information on Denmark's taxation of foreign pensions

Sorry, but I've been searching online for days now and not found this info.

I have a US pension and a dual US & EU citizen. I would like to live in Denmark for a few years. There is a double-taxation treaty between the US and Denmark that says my pension would be taxable in the US. (I read that to mean in the US only, but am not 100% sure about that.) Can anyone verify that it is taxable ~only~ in the US, or is it one of those cases where the Denmark tax authority would allow a credit against Denmark's taxes for amounts paid to the US?

For the amount of tax covered by the US-Denmark tax treaty: does it cover municipal tax and federal tax, or only the federal part of taxes?

As health care in Denmark is funded by tax, I assume I would not be eligible to use the medical system. Is there an option to pay a fee to join the medical system, or will I need to maintain private health insurance?

Thanks for any information you can provide!