Hawking radiation travels at "c"
I will elaborate below:
Hawking radiation escapes a black hole when one virtual particle in a virtual particle pair is created inside the event horizon of a BH (where nothing can escape) and one is created outside the horizon (where you can escape if you're moving fast enough).
If the particle pair which pops into existence are not photons, then even the one which is created outside the horizon would most likely not have enough speed to escape, and would be pulled into the BH along with it's partner.
Therefore Hawking Radiation should travel at c
Now, for your question about how black holes evaporate:
BH "evaporation" is sort of a misnomer. Nothing is really evaporating. The black hole just loses mass and becomes smaller.
When one virtual particle is created outside the horizon, it becomes real and just like any other particle in the universe.
However, the law of conservation of energy has to come into play somewhere (you can't just create extra energy out of no where).
So, the other particle, which fell into the BH, takes on a "negative mass/energy" and when the black hole absorbs this particle, it loses mass itself and shrinks.
So, nothing really evaporates. The BH takes on negative mass (which is the equivalent of losing mass) and a particle appears to be emitted close to the horizon as a result. The BH isn't returning mass back to the universe - mass is created as a result of mass loss within the BH.