Does it need any dependencies for full-fledged unicode character rendering, or can it read and render any platform's (Linux/Max/Windows) native font glyphs without much problems?
Can it import/render eps/pdf/svg inside a produced pdf file, or would I have to manually parse the image file, and redraw it in Cairo?
Cairo per se does not do "formulas" - it can work with the full set of unicode characters, but I think text support is better if you use the "pango" library along with Cairo.
As for importing a vector format, there is "librsvg" which works along with cairo enabling it to be used to render SVG files - this lets up to other libraries - maybe Tex itself, to render mathematical formulas themselves.
As for Pictures, yes, Cairo can import and draw raster pictures on itself.
I have an example of using librsvg with Cairo on this answer, though it is in Python, not in C. You will have to look for the online docs on both libraries to get examples of it working in C. (I remeber there were such, because there were no Python examples, I had to get this one working from the examples given in C).
