Does anyone know if it's easy to apply for a dual citizenship for their children? Also, is it worth it? And, which government office do you go to Immigration or DFA?

Yes that's correct, visit DFA. I've heard that government docs are now being expedited as per Pres. Duterte's order. Most of my Fil-AM friends have dual citizenships. But whenever they travel, they only present their US passports. Dual citizenship is also great especially if your plan to work here in the future so that you don't have to acquire working visa.

I heard processing of documents is being regulated by the new administration. Maximum of 72 hours will be the waiting time, they said. So for documents, I guess it will be easier than before, but with how consular offices process papers, that I'm not really sure. Maybe it depends on the embassy.