If I userstand correctly using the normal notation you are proposing:

GOT-xHEL-MAD-GUA//PTY-xMIA-LGA//JFK-xHKG-PER//DPS-xKIX-HKG-KTM-xHKG-xHEL-GOT

1. In general yes, but there is an exception to a second entry into Asia which, depending on how you interpret a comma in the rules, may make a transit in HKG between JFK and PER then a later entry to Asia valid. But I'm not aware of any recent reports of success getting such a routing ticketed. If you do then please let us know.

2. No, but if ticketed with specific flights then the LGA-JFK on the ground counts as one of your 16 segments. You may be able to get round this by having the ticket issued open-dated and to/from NYC; again this used to work, but no recent reports of success or failure.

3. Yes. All flights segments count towards your continent limits and both flight and ground segments count towards the overall 16 segment limit. Currently your route appears to have 16 total segments, and only 4 within Asia which is OK.