"A pilot may not credit flight time recorded as pilot-in-command under supervision (PIC/US) towards the flight time experience requirements for
an airline transport pilot licence."
This refers to PICUS time something we don't have in NZ, but a pilot coming from somewhere like OZ may have. Command practice is logged as Command Practice not a as P in C which is referred to here. I think PICUS might be logged as P in C. So PICUS time cannot be used toward to total P in C requirements needed for an ATPL.
(ii) 250 hours in aeroplanes consisting of 150 hours or more as pilot-in-command and additional command practice flight time as required;
NOTE: Command practice is time gained in accordance with rule 61.31(b). No more than 50 percent of the total command practice flight time may be used for paragraph ii) mentioned above.
What is being said here is that you must have at least 150 hours P in C and the remaining hours towards the 250 hour requirement can be made up with command practice time but you cannot use more than 50% of your command practice time to fill the gap. I.E. If you had 170 hours P In C you would need at least 160 hours Command practice to fill the 80 hour gap between 170 hours and 250 hours. However the Command Practice time still counts one for one towards the 1500 hour total requirement.
6)the pilot-in-command designated to supervise the co-pilot has certified an appropriate entry in the co-pilot's logbook,or a permanent record of the flight has been made by the operator.
Either the Captain signs each entry in your logbook or the company has a record of the Command Practice time which I think is supposed to have a record of the Captain OK'ing the Command Practice time. In the case of the company record you do not need to have a copy of this, but you do need to know that they do in fact keep a record.