Hello debskolmodin:
You have several questions here, which can all be addressed separately. We will do so in the following reply.
As to how to report earnings on your foreign (New Zealand or other) bank account or foreign financial account, the answer is that you will do this on a United States tax return just as you would as if the bank and the investments were domestic in nature instead of foreign.
In other words, whether or not you receive an actual Form 1099-DIV (for dividends) or Form 1099-INT (for interest) you will simply "pretend" that you did, and proceed to enter your dividends and interest in that manner. As such, you can can follow the mechanical data-entry instructions for each type of passive income, as described in each of the following links:
https://ttlc.intuit.com/questions/2952456-where-do-i-enter-my-1099-div
https://ttlc.intuit.com/questions/1899701-where-do-i-enter-form-1099-int
If you also paid any foreign (again, New Zealand or other) taxes on those dividends or interest, you can input that data on the very same 1099-DIV and 1099-INT input screens in TurboTax. There will be boxes provided there, in which you can indicate any foreign taxes paid.
Now then, reporting the income from your foreign financial accounts is one thing. Reporting the existence of your foreign financial accounts is entirely another. In other words, there is a "disclosure" requirement for every US taxpayer who holds assets in a non-US account financial account, even if the account or asset generates no taxable income. This applies to mainland US citizens, territorial residents, and expats, including those who never return to the US, but still maintain their US citizenship. Essentially, the government wants to know about your non-US assets -- how much and where you keep them.
In fact, there are two
separate disclosure forms that may be required; each also has different
reporting rules. One is known as IRS Form 8938, and can be
attached to the relevant yearly Form 1040 tax return. The other is FinCen
Form 114, which can only be filed via the internet. The following
Internal Revenue Service webpage describes them in some detail, and provides
their dollar value reporting levels:
https://www.irs.gov/businesses/comparison-of-form-8938-and-fbar-requirements
Form 8938 is included in
TurboTax. FinCen Form 114 is not included in TurboTax, and you would need
to access that reporting webpage separately, if your foreign financial assets
total over the limit(s). Note that you can get to the FinCen reporting
internet site directly through the above IRS link.
With that much explained, we now pivot to your question on health care insurance and the Affordable Care Act (a.k.a. Obamacare). For a full discussion of this topic, and the exemptions available to you while living overseas, please read the following post, where this matter is treated in detail:
https://ttlc.intuit.com/questions/3805932-does-foreign-health-insurance-count
Finally, please keep in mind that these answers only address tax matters from the perspective of the United States. They do not not purport to give any advice as to New Zealand tax law, or the tax system of any other foreign country.
Thank you for asking these important questions.
