1. Are their abilities trained like gnomes?
1.1 Is the growth rate of stats the same as gnomes?
1.2 What do different materials affect? e.g., Copper vs Steel automaton?
2. Do automatons need to be repaired if all they did was tend the farm and never get damaged?
3. Are prosthetics just aesthetic affect, as in a copper prosthetic arm is just a brown arm? Or do they affect skills?
1. Yes. They start out with generally more fitness and WAY less nimbleness than gnomes. This makes them not really good at being monks (punchbots) but they get over it because of 1.1
1.1 About the same. I got a full squad of them, and got them combat ready in about 2 years time (120+ Fighting skill). Sounds about the same to me.
1.2 The material they are made of gives the resistance to damage, similar to armour. Gold Automatons may look pretty, but they arent useful for combat. A gold autmaton jeweller can do his job just as well as a steel one though.
2. Non combat damage does not exist yet. Not for gnomes (hit yourself with your axe again, Fumble?), and not for autmatons.
3. Prostetics are the same as "natural" limbs when it comes to skill (which is a bit overpowered... but ok with the fluff, I guess). As with the automatons, gold limbs dont really hold up well in combat, and may be damaged/destroyed quickly. You can however replace them, should you craft better gear. The medic/mechanic (I do think he needs both tasks active to do replacements, but have not tested it out because my engineer is also my doctor) will choose better mechanical limbs for the gnome if better are available - and re-attach them right away.