Re: American passport?
Yes, my mother is american, never renounced her citizenship.
Both my brother and I went to the American Consulate in Antwerp to get our US passport.
That was 1976 for me.
I use it to travel to the US and also used it to go to Israel in 1979.
For the other countries, I haven't had to.
For Belgium, I'm 100% Belgian, but for the US, I'm an american living abroad.
And every year, I fill up an IRS form and send it to the US (but I don't pay taxes to the US as I'm earning much less than 70,000 $ a year).
Raoul