Search for a vacuum leak. The low idle is quite possibly due to a large positive fuel trim in response to AFR's skewing lean at idle; the revving up would be from it running into unmetered air from a leak in real time, before attempting further correction.
If its a vac leak, it could be anywhere along the intake tract all the way to the primary O2 on headers, but my guess is something under the hood. Check out those little resonator boxes coming off the intake tubes, or possibly even a loose hose clamp.
If nothing obvious is found, spray carb cleaner around the intake -- when the idle revs up you've found your leak.
The vibration while braking is either unbalanced wheels or uneven rotors as somebody else suggested.
Good luck!
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