My foot pedal for the rear brake does not actual the rear brake, however, the handbrake does work it normally. I looked at a parts diagragm and it appears I should be able to pull the back of the caliper off and there are some parts inside. Can I safely remove the arm from the brake and fix it without brake fluid or something else coming apart? Is there a common part that fails?

Also, the brake disk is not tight on the shaft (quite loose, flops around). Is this normal or should I replace it? My rear brakes work perfectly (besides the pedal), but seems like it shouldn't be that loose.

 

The sprocket should float on the shaft.
To get the rear brake to work adjust the jam nut on the end of the lever.