Well, it depends on some privileged APIs, of course. But we've tried to keep that API surface minimal.
In addition, the browser needs to act as a sort of broker between sites and the OS. Storing cookies and session data, showing notifications or dialogs, and entering fullscreen mode are just a few examples of this. (Note that most of these things aren't even implemented yet. Browsers are complex applications in their own right, even after accounting for the browser engine.)
We are deliberately trying to keep this to the bare minimum, and will likely try and find someway to standardize those few things we do if possible.
Servo's style engine is parallelized and scales nearly linearly with number of cores, and style time is a non-trivial amount of the total rendering time.
As for Firefox, later on this year we should see the integration of Servo's style engine ("Stylo") into Gecko, and going forward we should expect to see the two codebases share even more components. However, wholesale replacement of Gecko with Servo in Firefox isn't on the table at the moment.