Yes, so long as they've established permanent residence.
No.
She remains a Filipino citizen. Her US husband can petition for her, in which case, once approved, she becomes an American citizen. She can retain Filipino citizenship (hold dual citizenship) by applying at her nearest Philippine Embassy in the US (if she is based there).
You can join if you are an Australian citizen.
Yes, you do need to be a US citizen
A Jamaican can join the US Army if they have a green card or they are a naturalized citizen.
no
A filipino is a citizen from the Philippines.
Only a US citizen can enroll in the US military,you will need to become a citizen.
Simply by applying at the local recruiting office.
She can petition her mother, but the mother cant include her boyfriend on the petition, even if that boyfriend is the citizen's father,
Yes.
Yes a Filipino marriage is recognized in the US. I know this as an absolute fact as my brother married to a Filipino lady in the Philippines and they reside in the US. BTW, she is a naturalized citizen now and VERY proud of it.
Being already a Filipino citizen because of Dual Citizenship, You can stay as long as you like.