[Missing HGC status for some players]

No, each player has spent less than 3 seasons at FC Tokyo while U21, but three or more if you include FC Tokyo U23. Players who have spent three or more seasons at FC Tokyo proper correctly register as HGC. But it seemed like an oversight that these players don't have manually set HGC status or something like that because it was just a reserve team from what I can see from quick googling, unless that's genuinely how it works IRL

[Missing HGC status for some players]

No, they all have FC Tokyo or FC Tokyo U23 as the first club in their club history and spent at least three seasons there before moving to any other team.