2's complement is what most people expect these days. You don't actually run into 1's complement much anymore, unless you're dealing with antique hardware.
On the temperature, the answer is found in the ST forum:
https://my.st.com/public/STe2ecommuniti ... Items.aspx
Look at the threads with "temperature" in the title...the answer seems to be the same for all their similar chips, which I'll paraphrase:
OUT_TEMP_H is an 8-bit signed value which is added to a reference temperature to get an absolute temperature in degrees C. The catch is, the reference temperature needs to be calibrated by the user on a per-chip basis (or so they say....you would need a quantity of them to determine otherwise). So, given your result of 0x03 for 20C, that implies your reference temperature is about 17C.
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I'd think you can dodge the whole expensive connector issue by putting your adapter board at the other end of the harness, next to the main controller. All you need to intercept are SDA/SCL/interrupt, right? Power and common ground can come from whichever main controller endstop connector you plan to use.