Can I do quests i already did long time ago in hard mode

So basically when the primary quest is done in the campaign, i get hard mode unlocked and then I can do every single quest again whether I Have done it in normal mode or not? is that true?

no, most quests are one time deals (exceptions: the quest line in eye of the north is repeatable)....you can check out on wiki which quests are repeatable and which are not.
http://wiki.guildwars.com/wiki/Quest (pick the campaign you are looking for the quests in and it will tell you whether or not you can repeat it).
If you make a new character ---and have unlocked hard mode for the account in that chapter, yes you can do hard mode (once you reach level 20).....

When a quest is complete on a character, it is complete for good. The exceptions are, of course, annual festival quests and quests that are intentionally repeatable.

Thanks, good to know. I'm only doing the primary quests on the my new char. Waiting to unlock hm for factions

No, but its a feature id love to see. It makes sense that you would need to redo missions in hm, you should be able to redo the quests with better rewards as well.