Arduino One Wire Bus DS18B20 self developed driver missing bits or extraneous bits
I managed to find the bug and fix it.
I was missing that after the reset pulse the master must be in RX mode for atleast 480us no matter what, even if the presence pulse did occur and even if it's rising Edge did appear already. This mistiming did lead to the missing bits that were corrected with sending more bits until now (which in turn lead to the extraneous bits later on in the transmission).