Will US fight with China for the Philippines?

No. There is no appetite in the USA to defend the Philippines. The 1953 Mutual Defense Treaty is not worth the price of the paper it's printed on. Once the Philippines kicked out the US bases in 1992 things changed.

If the Chinese attack the Philippines call The Magnificent 13 and have them do something about it.

China and the Phillppines will never go to war. It's maritime incursions. But if it started to go down that route. The US would engage China at the UN level. If China ever attacked, the US is obligated to provide support.

They will use pressure to avoid the fight, Legally, US is suppose to support CHina's claim on the Islands. According to some treaties written by Spain, US, and Phillipines, their territory is defined and should not be able to claim the Shoals as their own. THere claim is recent, long after CHina made it known they own it and no one else contest it at that time. The actual question is if it should be administered By COmmunist China or Taiwan.

My assumnption is that US would try to do what it can with Phillipines.

it could be a new cold war, i don't think china or america is stupid enough to fight each other, however all the U.S air craft carriers are now based in the pacific, so watch this space i suppose, although personally i cant imagine them fighting anytime soon, well perhaps when oil becomes more sparse