I am new and have some questions.

Hi, I am new and there are some things which I don't understand:

1) I have made some quests/missions but, is there any way to see what I have done?
2) If you die you lose exp/money/items?
3) How much slots of inventory I have? I've seen I can buy more but if I but 5+ (for example) I will have them to the rest of my life^^. What is the limit of slots I can have?
4) Archers should go full dex? What skills must I raise?
5) How do I buy new hunt areas?

That's all, lots of thanks.

My name in game is Terakor, so you can pm if you want to play.

Hi, welcome to the community :)
1) There is currently no way to see them. In the upcoming 1.5 update, they said you will be able to see others' completed quests, so I would guess you will be able to see your own as well.
2) No
3) Each character starts with 50. You can buy up to 200 more (250 total). They will only count in the character you buy them for. Stash slots are for your whole account, so you don't need to buy them for each character.
4) Yes, full Dex. Read up in the archer class discussion for a lot of info on skill builds, but in general, Focus, Evasion, Blast Shot, Break Armor, and Shattering Scream are must haves IMO.
5) To buy additional campaigns, go to the store tab in your menu. First you need to buy platinum. Then use the platinum to buy campaigns in the "upgrades" area of the store (note that the whole store interface will change soon, so this only applies until 1.5 is out, then it should be easier to figure out).

World Map shows the number of quests you have completed. It is the two numbers with the slash between, like 19/19.
If you die while using an elixir the elixir will expire. Everything else is OK, though.
Archer, Focus and Blast Shot will always be useful so develop them first. There is a section for archers on this messageboard.

There is little more I can add to what Royce has already said. He's been here a long time and his advice is always good.

Lots of thanks