A few questions (In game and buying the game)

[Keydah]

This is wrong. As long as you link the alternate game license to the same service account, all the characters will be there. I play on ps3 and ps4, which require different copies of the game and different licenses. Everything is available on both of them.

Yeah, Steam doesn't work the same way cross-platform does. Steam is a PC license, and you can only have one license per platform - if you start your account on Steam, your account is and always will be Steam PC and can't be connected to other PC licenses (Heavensward has to be bought through Steam, you can't add a normal PC license to the account, etc...You don't need to use Steam to launch the game, but your account is still Steam) Even though no license was used for the free trial, of course, the account was still created through Steam.

So base on the classes (when you make a character), I assume you can't craft as an archer. What about materia? Would I be able to at least make that? How do I sell stuff?

As others have noted, you craft by going to the crafters' guilds, picking up the class, and then equipping their "weapon" - the same applies to battle classes. Talk to the receptionist, equip the weapon they give you, and you're instantly a carpenter or conjurer.

Gridania: Carpenter, Leatherworker, Botanist (gatherer) (battle classes are lancer, archer, conjurer)
Limsa Lominsa: Culinarian, Armorer, Blacksmith, Fisher (gatherer) (battle classes are marauder, arcanist, rogue)
Ul'dah: Goldsmith, Weaver, Alchemist, Miner (gatherer) (battle classes are gladiator, thaumaturge, pugilist - you need pugilist to 15 in order to pick up your archer's job, Bard, at level 30)

Materia: You don't craft materia - if you look at an equippable item, it has a "Spiritbond" percentage. Once that reaches 100%, you can right-click > Convert the gear (not all gear can be converted though) to turn it into materia. This destroys the gear and gives you a random materia. If you get a Savage Aim or Savage Might, you might be able to sell it for a pretty penny on the market board! There's not really any reason to meld materia to low level gear anyways as you outlevel the gear very quickly.

I don't remember if you need to do a quest in order to be able to convert gear into materia. If you do, the quest will be at The Bonfire in Central Thanalan. The coordinates (they appear in the top right by the map's x when you roll your mouse over the map) are Central Thanalan (23, 13). You must complete a level 15 or 20 (I don't remember) main story quest in order to travel to the other city states - you're an archer, so you're stuck in Gridania until then.

Selling stuff: You sell stuff by talking to your retainer (there are retainer vocates in the markets of all three cities to talk to to get a retainer) at the summoning bell, and selecting either "Sell items from your inventory on the market" or "Sell items from your retainer's inventory on the market" Once you have an item selected to put up for sale, you can view what others are putting the items up for by clicking the tiny page icon in the top right of the little price window.
You buy stuff by interacting with the market boards in city markets. This is where the stuff you put up for sale through your retainer shows up.

How do I get good equipment? What level do I have to be to start doing this? (I'm a lvl 16 archer right now).

At level 15 in the main story, you get to go into your first dungeon - Sastasha. There's pink and green gear that drop here - the green gear is unique, and the pink (aetherial) gear is good gear with random stats assigned to it. You should always check around and see what gear you can find from merchants and such before heading into dungeons to make sure you aren't wearing gear that's 10 levels below the dungeon, though, of course. Pink/green gear is good for 3-5 levels.

Due to the ability to change classes, having multiple characters on one account is kinda discouraged. In fact, one big reason to have all classes on the same character is so that if you get a dungeon drop while playing one class, you can use it on another one (dungeon drops typically cannot be traded)

Yep. There's no real reason to have multiple characters other than RP, playing on multiple servers, or, I suppose, as pack mules, though you'd have to jump through some hoops because of being unable to trade directly between your own characters.

[Kiki-Jiki]

I'll just check with support with the steam question just to be sure.