I think that if your father was (and/or still is) a US citizen, then you are also a US citizen no matter where you were born. It should be rather easy to get an american passport in the US embassy or consulate in the phillipines for you. As for your mother, I believe that she has to apply for a US visa or "green card" based on her marriage to your father who was/is a US citizen, or thru your US citizenship if you are over 21 years old.
Government of the Phillipines does not allow dual citizenship. She must ask for a permission to retain Hungarian nationality at the ministry of foreign affairs or immigration in the Phillipines.
The US recognizes dual citizenship.
she have to marry again in israeli
Yes, it is possible to have dual citizenship in the US. This means you can be a citizen of the US and another country at the same time.
Yes, it is possible to have dual citizenship while serving in the US military.
Yes, it is possible for a US citizen to hold dual citizenship with another country.
No. The US president MUST have US citizenship only.
By law, the US doesn't recognize dual citizenship (i.e. constitution prevents dual nationality) but somehow it always does recognize it.
Yes dual citizenship is allowed for US citizens.
Yes, a US citizen can obtain dual citizenship, which means they can hold citizenship in the United States and another country at the same time.
Yes.
Yes, members of the US military can hold dual citizenship, but there are restrictions and regulations that they must follow.