Answers from memory, you could email ASL directly with these and they'd probably answer them.
250 hours in aeroplanes as PIC including 100 hours of cross-country navigation of which 25 hours is to have been at night. Does General Aviation PIC count toward this? If so, I have 600+ hours of PIC in reciprocating single and twin General Aviation aircraft.
Yes, so long as some of that PIC includes cross country. Cross country for NZ means a destination more than 25Nm from point of take off (check CAA Rules for the exact definition).
250 hours in aeroplanes consisting of 150 hours or more are PIC and additional command practice flight time as required. Does any of my GA PIC or SIC time at a 121 carrier qualify as “command time?”
Think you're covered as above. Command Practice is the same as 'P1 under supervision', 'ICUS' or whatever the US definition of that is. If all your Pt121 time is logged purely as 'co-pilot' then no.
100 hours of cross-country navigation of which 25 hours is to have been at night. 50 hours of night cross-country navigation time command practice meets this 25 hours night cross-country requirement. How can I satisfy this? Does any of my SIC time at a 121 carrier qualify as “command time?”
As above. Was any (25 hours) of your cross country time in GA aircraft at night?
Other stuff:
Check the CAA website for a list of medical doctors (Aviation Info/Medical). There is one listed in the US (Scottsdale, AZ).
Long time since I did law but there are courses and books out there. The exam is web based at specifed venues, see the ASL website for details.
You might be challeged with the ATPL check ride if the type you fly is not on the NZ register. Email CAA for advice on that. Personnel Licencing probably.