According to Wikipedia, the main language is called Filipino now, but there's an interesting history of how it has been renamed and developed through recent years. I gather that present-day "Filipino" is mostly Tagalog, a predominant language of the islands, but with vocabulary added from other languages. In other words, there is such a language as Filipino, apparently.
I was interested to read that there are over a hundred regional languages spoken in the country, which should probably not be surprising in a nation of so many islands spread across a large area. The oriiginal non-Asian colonizer was Spain, and Spanish has been a lingua franca of the country through the years.
English is also listed as an official language, so it might not matter for day-to-day life if Melissa speaks only English. It's been my experience that people from the Philippines who come here speak English fluently on arrival.
I have no idea how Melissa behaved when she went over there, but if she'd been able to act tactfully, she could have positioned herself as tremendously useful to the Filipino skating movement, helping them to gain more spots for international competition. There must be such frustration on both sides. After all, Melissa gave up her American eligibility in hopes to get to more international competitions, and the skating federation of the Philippines must have seen their future walking through the door when she arrived--but neither outcome has come to pass yet.