By law, the US doesn't recognize Dual Citizenship (i.e. constitution prevents dual nationality) but somehow it always does recognize it.
The US recognizes dual citizenship.
No. The US 'officially doesn't 'recognize' additional citizenship(s) a US citizen may have.
If you apply for citizenship in another country your US citizenship is automatically revoked. The US does not recognize dual citizenship. You revoke it in writing at a US embassy, outside the US.
Bulgaria and Israel might recognize dual-citizenship for you but if you were born in the US (or became a naturalized citizen) - you cannot claim dual citizenship in this country.
she have to marry again in israeli
No. The US president MUST have US citizenship only.
Yes dual citizenship is allowed for US citizens.
Yes.
Spain does not have dual citizenship agreement with the US.
Some countries will claim the child has dual citizenship (see links below), however, while the US does recognize dual citizenship, any child born to US parents ANYWHERE is considered solely a US citizen
If you have dual citizenship, yes you can.
He will become a dual citizen of the uK and the US.