This could be the breaks needing replaced, could be a wheel bearing that needs replaced.
The rubber isolators in the engine mounts have worn out or the CV joints in the drive shafts are worn out.
You can tell if the transmission, in your 1998 Chevy Malibu, is going bad. If there is a whining or clunking noise. The transmission might cause your engine to install when you are stopped with your foot on the brake.
sounds like a motor mount is loose or needs replacing
if its an automatic change fluid filter in transmission!!
Yes, and that will cause shifting issues.
It could be the ball bearings or the ball joints or the breaks but not to sure but that's what it was on mine.
that is either your front right wheel bearing or your coil spring is turning need new suspension..$$$$
I would try replacing the fuel filter first.
It could be as simple as a stopped up fuel filter.
One way to know that a control arm bushing is bad on a Chevy Malibu is from the noises you will hear when you are driving. You will hear a clunking sound. The steering on the car will also not be as good as it once was. You could also experience drifting of the car as you drive.
If your pressing your brake when shifting it could be the neutral and park sensor. Or the linkage. If its the linkage you might have problems with your transmission slipping and shifting by its self or into certain positions easyly than others.
The 1999 Chevrolet Malibu automatic transmission shift cable has adjustment nuts on each end of the cable. Turning the adjustment nuts will lengthen or shorten the shifting cable.