Is engineering a profession like mining and refueling?

Yes, but also no. The main difference here is that for mining and for refueling, you have a resource or you gather a resource and then you sell it either to a player or you sell it to a trader. For engineering, you stand around in a ship and you press buttons. So it's a profession in the sense of, yeah, someone better pay you to do your job, else you will mess up their ship and it might not work. But that's it. So it is a profession, yes, but there is nothing to trade with.