If you have a check engine light you need to address that first. There are so many possibilities and the expense of doing them all would be very high. And none of them might fix your problem.
I would need a litle more information as to the circumstances so as to make a diagnosis. The fuel filter should be changed every two years.
That would depend on which model year of Chevrolet Malibu ( both rear wheel drive and front wheel drive versions have been made )
if it tends to sputter and have no power i would suggest the fuel pump. it it is only after the car has warmed up, or a while after you start driving it might be the ignition module.
bad ground
The coldness
The model year would help. Chevrolet has been building the Malibu from 1964 to 1983 and then again from 1997 to present.
Lots of reasons, but mine was the fuel pump was bad. It would overheat after driving maybe 15 minutes, then I would let the car stop for an hour or two and it would start back up.
It would be to your advantage to buy a Haynes Manual as there is plenty of information that would be very helpful.
That would depend on the year and engine size. If you do not see a distributor then it is distributorless ignition.
A Chevrolet 2013 Malibu LS costs about $169 per month on lease by Chevrolet themselves. Lease costs changes according to make and model. For further details visit the Chevrolet website.
If none of them are working then you could have a master switch or relay defective.
It sounds as if you have either a power or ground problem at the motor.