I know that faction leaders have certain access to the faction members accounts. Exactly what info are they able to access? Are they limited to altering rank and various naming aspects, or can they see members personal inventories and credits history?

They don't have any "access" to members' accounts. They are able to do simply what you've said. They can alter infofields, and assign/unassign faction-owned entities to members.

They can also see your faction join date, last login date, email address connected to your account, and some other unimportant stuff. They can not see anything in your inventory, or your location.