Well, there is no law prohibiting to go on a vacation while waiting for your naturalization certificate. However, they can deny you re-entry to the US if they find you are inadmissible; but this unlikely if you are a permanent resident and have not been convicted of a crime while residing in the US. If you have, then you should consult an attorney.
Yes, you can apply for dual citizenship in your home country.
you can have two citizenships
If you meet the citizenship requirement of the foreign country/state you are living in, then yes you can apply for citizenship of that country/state.
Chicken
You will have to consult an immigration attorney. In most cases, he will have to leave the country and apply for a visa. This could take several years!
Apply at the nearest embassy or consulate of your country of citizenship.*Your case would not be approved usually if you do not have another citizenship.
SPAIN!!
Apply for an Israel Citizenship by contacting their embassy in your country.
To apply for dual citizenship in the USA, you must first be a citizen of another country and meet the eligibility requirements set by both the US and your other country. You can apply for dual citizenship by following the naturalization process in the US and also by complying with the laws and regulations of your other country regarding dual citizenship. It is important to consult with legal experts or immigration authorities to understand the specific requirements and procedures for obtaining dual citizenship.
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.
The easiest way to get the to get UK citizenship is to be born in British but because you have not accomplished that, then you second option will be to get a working visa, then apply for Indefinite Leave to Remain after staying in UK for 5 years and then after 12 months apply for citizenship.
No, they are US citizens.