Your question doesn't make much sense. If you are a citizen you don't have to "gain citizenship" you already have it. That said, if you are a non-citizen living in the United States of America and have lived there for Five (5) years you can apply for citizenship.
at least 5 years
US and UK allow Dual citizenship. A person can be a US citizen and a citizen of UK if he/she desires to. But if a person applies to get naturalized as a citizen of UK when he/she is already a US citizen, then it will lead to losing US citizenship.So a person can have US & UK citizenship as long he/she is not a naturalized citizen of UK.
Teapots
No. Not even marriage to the father grants gives you citizenship. You have to apply for naturalization.
The process for the individual trying to gain citizenship will stop.
You must be a natural born citizen of the US.
He can marry the US citizen but he won't gain citizenship through her n he will still b deported.
She can, but she will have to give up her US citizenship, not a good idea.
Being already a Filipino citizen because of Dual Citizenship, You can stay as long as you like.
Its possible
It makes no difference how long a US citizen of ANY age is out of the country. "Once a US Citizen, always a US Citizen." -UNLESS- you renounce your US citizenship and become a citizen of another country. However, since the question is about a 'minor' child that eventuality should not arise.
The citizenship process is very hard and long.
If you are a US citizen, there is no law regarding this. You can stay out of the US for as long as you wish, you will never lose your citizenship and can return anytime you want, as long as you can prove you are a citizen.