Gonna bump this to ask if any resolution was found. I'm having the exact same symptoms, #1, #2, and #3. Recently replaced O2 sensor with new Motorcraft part, but still throws P0133. I'm in the process of datalogging the problems with Tom.
Mine: 2006 Mazda3 s GT Hatch: 115k, Gray, Manual
Gone: 2002 SVT, #1654
Hers: 2012 Focus Ti Sedan: 55k, SGM, Manual