a FC helps, or an apartment. The coloring is done by feeding your stabled chocobo certain fruits like marmook pear, ogamarro berries.
To rank up past 10 it needs to be max exp and fed a Thavnarian Onion(this works even in the open world)
for every rank above 10 you need another Thavnarian Onion, the max rank is 20
Cant command the chocobo, the tooltips have been wrong since 2.0. Its sad honestly.