It could possibly
It could be as simple as a stopped up fuel filter.
The 1999 Chevy Malibu with the 2.4 engine does not use a PVC valve. Instead the system uses an oil/air separator that can clog up and cause the same symptoms.
The fuel filter should be replaced every 2 years. It is possibly stopped up.
The coldness
Unless you have a scanner or the equalivant then you think you reset it when in reality you have only had to reset the clock.
There are pages and pages and items that can cause a check engine light. You need to have it checked for codes with a scan tool. After repair light can be shut off with scan tool.
I am almost certain that the brake has nothing to do with it. I surely would check the fuel filter and replace it if you haven't in the past 2 years. If the check engine light is "ON" then have it diagnosed.
There are several things that can cause your 2005 Chevrolet Malibu to run rough. The fuel injectors may need to be cleaned. The air filter may need to be replaced.
I'd change the fluid and filter, but no guarantees.
Check the battery cables and ensure that they are CLEAN and TIGHT. That is the most overlooked thing.
Possibly the pressure cycling switch.
The 2005 Chevrolet Malibu axle nut torque specification is 60 pounds. Over torque in the axle nut will cause the will bearing to fail.