How well do Filipinos speak English? Listen to all the heavy accent, so after learning English from Filipinos, will there be a big obstacle when communicating with foreigners in the future?

It does have an accent. Are you learning from ordinary Filipinos or from Filipinos who specialize in teaching English, just like China, there are those who speak pure English. Before you learn from someone, listen to see if there is an accent and if there is an accent audible. If you are really learning Filipino-style English, there is definitely an accent, and the other side will know when you communicate with Europeans and Americans, but generally do not discriminate, just may think you are Filipino, communication will not be a barrier