The rest of the performance work was untied from Rust, as far as I'm aware.
Upcoming somewhen after 57 is also WebRender / Quantum Render, which should give a significant boost to FPS. Basically, if you've ever wondered why your gaming PC can render out giant space warfares at 120 FPS, but your browser starts stuttering when that super cool menu animates itself, WebRender is going to fix that in principle.
So, there's still going to be other problems, like JavaScript performance just not being on par with compiled code, but it should bring us a lot closer to the FPS that you'd expect.
(To throw in some technical terms, in case you want to research: Browsers so far used Immediate Mode to draw things, whereas WebRender and video games use Retained Mode.)
And WebRender was architectured as part of Servo, so is also written in Rust, but I can't tell you, if Rust really benefitted work here, or if it just happens to be written in Rust.
This illustrates the sort of difference we're looking at with WebRender: https://www.youtube.com/watch?v=u0hYIRQRiws
(Mind, though, that the video is more than a year old now. Firefox 57 should also already perform a lot better than what is shown in the video. Then again, WebRender is VSync-capped in the video...)
Was it easier to write code for the replaces parts with Rust? If yes in what way?
Any data/metrics regarding bug counts on Rust vs C++ for the replaced components?
Here's a funny one for the multimedia decoder: https://hacks.mozilla.org/2016/07/shipping-rust-in-firefox/
Rust itself is more about preventing bugs and security problems than improving performance.
So yes, it's not like just writing it in Rust will make things faster. It's that Rust makes it easier to do "improved algorithms, gpu leveraging, and system design" in the first place.
That also said, its true that there's a lot more to 57's speed than just the Rust work; the UI work also plays a huge part for example, given their focus on user percepted speed related issues.