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.
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.
You must be a natural born citizen of the US.
The process for the individual trying to gain citizenship will stop.
She can, but she will have to give up her US citizenship, not a good idea.
He can marry the US citizen but he won't gain citizenship through her n he will still b deported.
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.
Yes, it is possible for a US citizen to hold dual citizenship with another country.
The citizenship process is very hard and long.