As long as you don't fly to the US. US citizens need a valid US passport to enter the US, even if they also have another passport[1]. Entering the US is literally the only thing I use my US passport for and the only reason I get it renewed.
[1] I guess you can try to lie on your visa/ESTA application and hope they don't notice, but I wouldn't recommend it.
US citizens are required to report all worldwide income for taxation. Elsewhere, requirements to pay tax generally depend on residing in the country for some number of days per year.
> do you need to present your US passport when leaving the US and your foreign one when arriving some place?
Yes.
> Would you have to reveal at the border that you are a US citizen?
At the US border, yes. If, say, you have a European passport and you're entering Europe, you present the European one.
Taxes? Annual reporting of some such?
What happens if your American passport expires, can you fly on whatever foreign one you have only? Or do you need to present your US passport when leaving the US and your foreign one when arriving some place?
Can you fly back into the US only using your Spanish passport?
Would you have to reveal at the border that you are a US citizen? Or just show your foreign one and not mention US citizenship?