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.