Not if it's a .max file, you'll need to export to a different format preferably .obj
If you got animations you'll have to ask someone over here about that as I do not know all the issues involved with exporting those.
Yep fbx does bones, animations, cameras, lights, materials just about everything in a scene that can be translated over is. It's the format they came up with to port stuff back and forth between Max, Maya, mudbox motion builder. However once imported it uses it's own systems with their specific look and function so you will want to experiment to make sure everything is useable.
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If you got animations you'll have to ask someone over here about that as I do not know all the issues involved with exporting those.
Good luck.
There's also COLLADA if OBJ can't do what you need it to, though FBX should work.