New to DAOC

This is a huge question but I'll try to help.

-How many profession are there?
Alchemy, Spellcrafting, Tailoring, Armorcrafting, Weaponcrafting and Fletching are the primary ones. There are sub skills that go along with those (some are shared) that are used for salvaging (and there are some like Gemcutting which do nothing).

-Is it really useful? (Best way to make gold?)
That's a hard question to answer as it depends on supply and demand, and the fact that getting to the "high enough" skill of each of those costs a different amount of time and gold. The simple way to make money without making items to sell to other players is to get high enough in the sub skills (usually metalworking and woodworking) so that you can salvage items -> craft the materials you got into "trinkets" -> sell the trinkets to a NPC.

-is there an auction house in the game?
No, but there is player housing. If you have a house you can buy and place a Consignment Merchant and then place items you want to sell on that merchant for a price. Players can use a "search" merchant that will search all the consignment merchants out there for items. Then they can either buy it directly there (for a 20% fee which only comes out of their pocket, not the sellers) or they can travel to your house and buy it without a fee.

-How does the profession system works? You level your skills as you craft?
Recipes come in colors grey->green->blue->yellow->red and the lower (green) a recipe is the less chance you will have when crafting for you to raise your skill. So most players will usually make yellow or orange items. Higher items (orange and red) have a higher chance of failure. Failure alone is fine, and is just a loss of time. But the higher the recipe is to your skill, the higher chance you have of losing some materials when you fail, hence why players don't craft red items much.

There is so much more about crafting, and a few unique things to this server but that should be a start.