Regarding Problem 1, I've checked continuity on all of the traces coming off of the SWIM, and I can't find anything amiss, so I'm regarding the bourns filter as suspect for now, and will have to wait for a replacement.

In the  meantime, I'm at a loss regarding Problems 2a and 2b.

The logic board has been thoroughly cleaned and looks factory fresh now. What else could this be? RAM? A bad solder joint somewhere? Rotten trace?

I don't want to try to check every single trace on the board...!