In what image did you see a TACPAD on Hazel's left wrist? Thanks!
There is going to be a minor update to the Spartan page which will explain a lot of ranks for Spartan-IIs. Tbh it will make us not know most of the ranks for most of them.
The tldr if we haven't seen them successfully auged prior to 2526 then it's entirely possible they had to go through Rehabilitation and thus we can't say they share the same rank as the others who passed augs without needing to be Rehabilitated.
Her status is dubious at best but most likely not canon, therefore she isn't listed.
The tldr version is. Keiichi could of been left on Harvest, taken to Arcadia, still on the Spirit, or is dead.
Carris is unknown, they were kidnapped. But if they survived augs or not is unknown.
Naomi and Omega are unknown. Its possible they were on Reach during its fall but its hard to say.
About about Battle Born, stuff in general will be updated when we all read though the book and fully understand stuff. Its only been out 4 days like lol.
Btw our discord is a better place to ask questions of this nature.