Retiring in Belize or Costa Rica and having HIV

One's medical condition will likely not come up until one applies for residency, work permit or QRP.
Call or email one of the pharmacies and/or hospitals in Belize City to see what medications are available.
Your income is still taxed in the US, even if you reside in another country.

But if you obtain dual citizenship, you are not taxed in the USA.

I believe as long as you are a US citizen, you are subject to taxation on income earned worldwide. (Over a certain amount)

one may want to check with a tax accountant ....it is my understanding that even if you have dual citizenship, as a US citizen all income worldwide is taxable by the IRS.  And one must file a Federal Tax return yearly.

I have dual irish/ American passports/citizenship.   How will I be taxed.   Thanks in advance.

One can only be taxed on income, so if no income no tax wherever in the world. If all your income is generated in the states it will be taxed in the states as per normal  Your income generated overseas will be reported by your Bank to the US tax office and you will have to put it on your tax forms when you do them by April. Once you have an active tax ID No in the states the tax system can and will try to tax all monies wherever in the world. Most  European countries have arrangements in place to avoid double taxation.