Does sorcerers in Conan have/or can obtain any familiars? If so, in which book I can read about obtaining them, what do they provide for their master and so on?
Are such familiars just normal animals? Or magical beings if they do exist?
Probably not, but it’s your Hyborian Age so do what you want. The ‘power base’ for sorcery is Lovecraftian entities, so the only thing I could suggest is Brown Jenkin:
Not in the D&D sense if that’s what you’re thinking. Some creatures have the Familiar (X) ability as described on page 308 of the core book. Some others have Patron and can teach spells.
What they don’t do is serve as trap detectors or provide combat assistance as in 5e.
There is no special rule, skill or talent that sets a familiar like you might know from other roleplay systems (like D’n’D and/or Pathfinder) that do apply buffs and bonus in sorcery or combat for the character.
But there is the skill animal handling with its talent tree (see also the expended talent tree from “Horrors of the hyborian age” and the additional information). With this skill and its talents you can create a familiar for a sorcerer or any other player character and so have the animal that is accompanying your sorcerer and act like a familiar.
See core book page 58 - 60 and horrors of the hyborian age page 110 -112.