Originally Posted by msantos

In all likelyhood the vibration you experienced was due to the vehicle warm-up. It is normal for the vehicle to rmp its way to 1500 for the first few minutes of operation especially in cold mornings. However the rattling is not normal.
It may very well be that something is making the rattle such as a loose heatshield or even a rock lodged in any of the heatshields under the vehicle. A quick inspection (typically free) by the dealership should fix that.

In regards to the fluid dripping from the exhaust: This is a very common occurrence-particularly during vehicle startup as well. What we often see is water dripping - not gas. The air that gets used in the combustion process has a certain amount of moisture and gets expelled in this way.

Cheers;

MSantos