About to give up on this car
Sounds like you might have a synchronizer or two have are wiped out, and might be missing a tooth or two on one of your gears
Jack it up, crawl under there, grab the tailshaft housing, and give it a shake to see how much it moves. Visually inspect the trans mount for signs of failure, eg. cracks in the rubber or worn metal showing.
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Grinding on any transmission calls for remove and find out where and why if the tranny mounts prove that they are not allowing the tranny to move around. But since you are having problems in various gears then i would say its safe to assume that your manual needs a rebuild.
Run a code scanner in realtime monitor mode and watch and see if your ignition is being retarded during your "very nasty rattling" events...that will tell you if the knock sensor is "hearing" your rattling noise.
The vibration and transmission noise has nothing to do with setting these codes. While by the sound of it you definitely need to have some tranny issues fixed I can assure you that it will not get rid of those trouble codes.



