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In general Filipinos are almost universally nice to everyone, there are some exceptions with older people and certain countries (Japan, basically). Many people from the US retired or work here and Filipinos will generally show deference to any westerner and treat them politely. Most Filipinos I know are aware of the history but it doesn't really colour their current thinking, they just default to treating people politely.
Be aware that Western = Rich in many peoples minds and that will make you a target for scams and things, but that's not specifically a US thing.
I don't think I can answer your second question expect by saying just be polite, don't take advantage of peoples kindness, treat people with respect, try and get to know people and their life. Be aware that many people may not want to talk about politics or the history of the country, partly because it doesn't affect many peoples day-to-day lives as they see it and partly as they would want to avoid arguments if your views differed.