EGR is Exhaust Gas Recirculation. It is an emissions system that directs exhaust gas through a tube to your intake manifold at cruising speed to help reduce emmisions, unfortunately the tube diameter is fairly small and after time/mileage it cloggs with soot and gunk which can cause a check engine light for EGR malfunction. That is not the case as you described with your car, at least for now, lol.

Your brake problem seems odd, would most likely need to drive it to fully understand your complaint.

For the engine noise, check your belt shock bushing at the top. It's a long black shock(about 6in.) that sits just to the driver's side of the valve cover. It helps reduce belt tension fluctuations and it is very common for the bushing to wear and make a knocking sound. It can easily be mistaken for a lower engine noise. Just put your finger on the end of the shock wiith the car at idle and see if the noise gets better.

For your transmission, I would recommend having it serviced if you haven't lately, but I would stay away from fluid additives. Just my opinion.