The bottom engine mounts are the usually the ones that break.
Do this in a safe location
Press the brake firmly with your left foot (apply the parking brake also)
and with the transmission in drive and the right foot press the gas pedal quickly & release. This loads the engine mounts and if the mounts are broken will cause the engine to jump or create thud noise/feeling. Do above procedure in Reverse also as it will load another engine mount on the bottom.
As for the surge when coming to a stop. See if the engine surges when coming to a stop when you shift into neutral before the surging usually happens and let me know if you can still feel the surge.
Thanks for the question.
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Tuesday, June 10th, 2014 AT 1:42 PM