Vibration felt on the gas pedal and steering wheel of my 2003 Mazda6i

My best guess is that you've got an un balanced tire, that would explain the vibration... and the extra fuel economy is coming from the fact that you're getting to speed more carefully trying to figure out what is wrong with the car? Slower acceleration makes for Higher Milage... Can't think of much else that would cause a vibration like that...

I'd mostly agree with Chris. You're vibration most likely is in a tire. Could be out of balance, maybe lost the balancing weight off of the wheel, or it might be out of round, broken or shifted belt, or bulge. Be sure to have your front-end checked also as vibrations like that can wear out suspension and steering parts early. "Also, my car has also been experiencing a low-rpm output (about 700 rpm) when the engine is idle." What do you mean by this? Is it surging? If so, check for vacuum leaks, cracked or disconnected hoses. An easy way to do this is to LIGHTLY spray some starting fluid on lines and hoses while the engine is running. If the rpm's suddenly jump while you are spraying, that means there is a hole around that spot where the engine was able to suck in the starting fluid. BE CAREFUL to do this when the engine is not too hot, and DO NOT spray on the exhaust. Starting fluid is combustible, I've never seen it happen, but it can catch fire (have to add that disclaimer for certain people). For your fuel economy...how have you regulated the amount of gas you put in? This might sound silly, but if you're always putting $20 in the tank to get to halfway, since gas prices went down so much, $20 would get you more gas, but probably not so much as to make a noticeable difference on your gas gauge. Check your receipts to see how many gallons you've put in it. Maybe it's not better mileage, just more gas goes farther. If that's not the case, then again I'd agree with Chris.

the low idle could also just be because of the cable that controls the idle speed. If it is just a little too loose it idles lower. I had the same problem with my car. Its a ten cent repair. I agree with the others about the vibration and gas mileage. vibration is to be expected after aggressive driving though, epecially if you corner really hard. Good luck!

THe vibration could also be caused by snow getting packed in between the rotors and the wheels. We have had this issue a few times what with the snow in Michigan.