I think one can verify the fingerprint by other means, e.g. phone

Another way to understand what e.g. 0xFE means as a signed integer is to just add a number until it equals 0. So, 0xFE + 1 = 0xFF, not zero. 0xFE + 2 = 0. Therefore, 0xFE is -2.

Yes and the formula to negate x can be simplified to:

0x100 - x

dropping the 9th bit (assuming 8 bit)

Uh, it's simpler than that. 0x0 is 0. 0xFF is -1. What more is there to "understand".