You've gotten a lot of good advice, pointing you in the right direction. I will add to the discussion by saying that if you have at least one light working, you probably don't have any major issues to consider. Sounds like you have a combination of small occurences. Pull all bulbs and compare the internal elements (filament) to the known good bulb. If any don't match the known good one, replace it. Most of the time, the high mount (third brake light) bulb is blown.
The other problem sounds like you may have corroded or contorted prongs in the bulb sockets themselves. A very simple fix with a good quality pick, scribe, or any other sturdy but small-tipped tool, and lot of patience and eye for detail should do the trick.
To diagnose a little further, take the known good bulb and place in the sockets that are not lighting up. Upon depressing the brake pedal, if the known good bulb does not illuminate, then you know that socket needs repair or worse case scenario, replacing.
Hope this helps.