1. According to the rarity of the equip, it tells you how many enchants the item can have. Such as green having one enchant, blues having two, orange having three?, red having four? I don't remember the exact numbers, but the more "rare" the equip is, the more enchant options you may have on the item, of course there's exceptions such as Coli equips always having 0~2 enchant option. Plus on top of that, you can enchant one stat that isn't currently either of the options. Just say you get a green item, which means there should already be one enchant on it, you can choose to level up that current enchant, plus you can enchant one extra enchant aside from the option you already have. It may sound confusing, but if you don't understand something, let me know.
2. Do you mean Crystal Mine? I don't remember a Crystal Island. If you're asking about Crystal Mine, you need a ticket to get in. You can get them from players selling them, or you can go to Ant Cave and hunt the monsters there, they might drop some. They're timed tickets, so once you use it, you'll be teleported to the map and stay there for the indicated time. There are monsters in the mines that can also drop the tickets as well.
3. It's two sets. The top two slots are your main setup, the bottom two are if you want to dual wield weapons, so you basically just setup another set of weapons you'd like to use, and you can change from one set to the other by pressing tab.
4. All pets, at least that I know of, are timed. If the time expires, all you have to do is buy Pet Chargers, either from players, or from the fashion shop.