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I wonder where Rust and servo fit here. Will they be able to "swap" some parts of Firefox with others written in Rust?

There are already bits of Rust code in newer builds of firefox, I think they'll ship first in 47 or 48. https://wiki.mozilla.org/Oxidation

Servo is a fantastic research project but it will be a while before it is "production ready".

They have done so recently, mp4parse-rust is a replacement for the old mp4 metadata parser.