In HKG you can checkin at the Airport Express station in HK Island or Kowloon on the day of or day prior to departure (for all destinations except USA). I think they would regard 00:35 as late in the day not early, so I believe you could, for example, check in at 07:00 on Thursday for a flight leaving 00:35 on Saturday.

I don't think there is a maximum at the airport within its opening hours, and you can online checkin up to 48 hours ahead.