Does muffler play any role in car performance?
Becouse I heard if muffler is in bad shape the car wont perform as it should...

the standard muffler is build with a series of passages and chambers, to slow down the gasses in order to absorb as much noise as possible.

ofcourse slowing gasses down means losing performance (as you want to let gas exit as fast as possible). a freeflow allows gassed to flow unrestricted (hence the name) and will give you better throttle response.