Start of the game
 

When i started the game the first guy told me i was not very good at killing dragons and should become a Treasure Hunter. Does this have any effect on the game later on ?

Also: the chests that can be found in the tactical areas. If i win the battle and don't open it, will it just dissapear or will it get autolooted? Can anything usefull be found in those chests so should i make it a priority to open them?

In any case you will be a Treasure Hunter and it won't influence the game.

And about chests on battle arenas: open them if possible, as there you can find gold, scrolls, artifacts, runes and etc. and you can open them only during the battle.

yeah adds a bit more strategy to the battles i think, cos it does waste an attack opening em. I found the officers baton in a chest and a few spells and the odd rune but 99% of the time its just money. I always try and open em tho.

And it is usually best to get them ASAP for the opposing forces may gather the loot themselves.