Why are the RPM's fluctuating when idleing and braking

Hello, first -- you have the luxury of available clues as noted by the "check engine light" being on. Obtain a diagnostic tool (or enlist the help of a trusted technician) and determine what failure codes are stored in the engine's processor. Whereas they may or may not relate to the concern you are experiencing, it's a great place to start, in that they represent "known" issues and those should be addressed before guessing further. If I had to guess, I'd say you likely have lean codes in the processor and that you have an air intake or vacuum leak.