Its not clearly defined in the book as far as I can tell, but what skill is used to repair a drone? Industrial Mechanic? I saw a specialization for that, for Robotics... Is this correct?

Also are there costs for repairing a drone? or is it assumed that your repair kit has enough materials to do the fix.

I'd go with automotive for most ground drones; it's got anthroform as a specialization and applies to some hovercraft as well as anything tracked or wheeled, so that should cover just about any ground drone in the book, although you'll obviously need aeronautics mechanic for a fly spy and other flying drones. As for what's necessary to fix one, that's pretty much up to GM fiat; in my case I just base it on what tools the character character has purchased. If a drone is merely damaged rather than disabled you can fully repair it with a Kit but you'll likely need a Shop to repair a drone that ran out of boxes entirely. If it took overflow in excess of body score I figure you either need to replace the drone entirely, buy new parts or have access to a Facility. Ridiculously catastrophic damage like taking enough damage to be insta-gibbed into higher-than-body overflow from a single attack (much like an instant death for a character) means even a facility can't save it (or, at least not cheaply enough to be better than just buying a new one), although that obviously doesn't come up often even for tiny drones and has never happened in my group at all with a vehicle. A long enough campaign and I'd probably make people buy new kits and shops; hasn't come up though, I've really only been gming for the last 6 months or so, up until then I was usually just a player.

I agree that the appropriate Vehicle Mechanic skill would be what I would use for repairing Drones.

Use the vehicle mechanic skill corresponding to the vehicle pilot skill.

In the span of a city adventure what use would the Industrial Mechanic skill have? I'm not seeing a pro in taking it.

Want to hack an elevator?

You´ve never build a team fortress, or have you?