I say whenever one asks a question motivated by a desire to understand the human condition better, one is asking a philosophical question. It's the motivation for asking, not the content or format of the question, that makes it inherently philosophical. Remember that the goal of philosophizing is the cultivation of wisdom. If one comes away from a discussion wiser to the state of the world and one's place in it, then it matters not whether a final answer to the question was ever settled on. It's the process of pondering and debating, and the resultant appreciation for the depth and complexity of the issue, where the magic happens. This is not to say that one should never strive to take a stand on any philosophical issue -- if you find one side of an argument more convincing than all others, by all means hold it. But remember that solving all the mysteries of the universe isn't the point, and it's not nearly the tragedy it seems if you can't make up your mind on many philosophical issues.
Granted formal philosophical schools have rules about what subjects are worthy of consideration, and how a question should properly be asked. The Analytical school, which dominates academic philosophy in the Anglophone world, prefers narrow, specific questions composed of words with precise definitions -- a far cry from the broad-sweeping and ethereal discussions one finds in folk philosophy. These rules are codified and enforced in these schools for pragmatic reasons, for the same reason debate clubs have rules -- they allow people who don't know each other and don't agree with each other to nevertheless discuss heavy topics civilly and without talking past each other.
Whether the Analytical school is a de facto extension of science is highly debatable. It's certainly the philosophical school with the longest and most trade-friendly border with science. It defers immediately to science for all things successfully observed, measured, and tested, and agrees with science in valuing precisely defined terms and parsimonious conclusions. But it is not science, because philosophers do not run controlled tests and collect data sets on their hypotheses. Instead, they support their hypotheses with logical statements that they invite the reader to assume as given / true. These statements may or may not be supported by scientific evidence, or even testable. I think you could more easily call strict Analytical philosophy a sort of mathematics, than science.
