Did it all work properly before?
Or is this just a culmination of a bunch of problem you decide to ask about all one time now?
I would start with the "CPU" - I think all power signaling the turn signal, whether it's the turn signals themselves or the hazards, do go through this black box.
Cold solder joints are typically the problem - resoldering them usually fixes all the headaches.
If the problems are not connected with each other, then read on...
Brake lamps not turning on when stepping on the brake pedal could be bad brake switch.
No reverse lights could be bad reverse switch on the transmission.
-Ted
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