if my alternator was tested and functioning properly why does my battery and brake light keep coming on in a 08 Nissan Altima 3.5

I would get the alternator looked at by a professional. Just searching around on this site, there are a number of reported issues with the alternators on various Altima model years. Some appear to be mechanical failures, where presumably the charging system was ok but the pully failed, sometimes damaging the belt and/or other components.

It's also possible for the charging system to appear to be outputting good voltage at idle, but once there is significant current load on the system the alternator might fail to keep up with the demands of the system. This requires more than just a volt-meter to test.

The initial battery dying could itself be a symptom of a faulty charging system as well. And if that's the case, you would see similar behavior where things seemed "fixed" for a while when the new battery was installed, but as the alternator can't keep the battery charged, you'll again start to see more electrical symptoms over time.

as a quick check I would start the car and remove battery to check if car can sustain itself on just an alternator also check for voltage change.

It could be that you installed a new battery and while checking for voltage out from alternator you receieve battery voltage