Does philosophy still have a place next to science?

Philosophy is more fundamental. For example, notice that some "philosophies" reject the theory of evolution altogether.

The fundamental issues of philosophy -- is there a world that follows natural laws, and can we know it and if so how? -- precede science.

Absolutely! There are many places where philosophy can intersect with science, and in some places philosophy has helped science along.

Take mathematics, for instance. Before the 20th Century, mathematicians were basing arithmetic, the foundation of all mathematics, on certain "self-evident" axioms, like 1+1=2. If you assumed certain things, they argued, math can be built from the ground up.

Several philosophers, like Gottlob Frege and Bertrand Russell, came along and asked the very relevant question "Well, if it's so self-evident, why should we have to assume it? Why can't it be proved?" In response, Russell (a philosopher) and Alfred North Whitehead (a mathematician) wrote Principia Mathematica in 1910. In it, they proved that arithmetic can be built from the ground up using logic. Math basically has a sound foundation in logic; it is derived from logic, in a sense.

There are many other cases where science and philosophy have intersected. In general though, they are two completely different subjects that ask different questions. Science asks "Why does gravity work the way it does? How does a star work? Where is the edge of the universe?" Philosophy asks "What is the nature of right and wrong? How do we know if something is sentient? Where is God, if there is one?"

These are, for the most part separate questions, which sometimes intersect.

Yes. They are inextricably linked and the philosophy of science is itself defined by science under the most reasonable paradigms that define human thought.

The scientific method allows us to discard many silly notions of the philosophical underpinnings of the world, but as scientists we must remain skeptical of all our thoughts and paradigms.

It is in this skeptical role that philosophy plays a critical role in the big show - allowing us to question the very things that seem so clear to us after the application of the scientific method.

Hmmm - I'm pretty skeptical of THIS answer.

Only when philosophy does not contradict science.