Tiny Tuner 2 - nothing showing up on Serial Monitor except "Monitor starting"

tobitop:

  1. on the serial monitor it says "Knock Bang fault" which makes me think of an error

Have you checked the Knock Bang source code?

  1. TinyTuner 1 says 0x80 and TinyTuner 2 says 0x62; shouldn't the values be more or less identical concerning one µC?

I've read the calibration chapter in Atmel's datasheet.

Read it again (emphasis added)...

ATtiny85 Datasheet:
The CAL7 bit determines the range of operation for the oscillator. Setting this bit to 0 gives the lowest frequency range, setting this bit to 1 gives the highest frequency range. The two frequency ranges are overlapping, in other words a setting of OSCCAL = 0x7F gives a higher frequency than OSCCAL = 0x80.

The figure labeled Calibrated 8 MHz RC Oscillator Frequency vs. OSCCAL Value will help.