In scenario set up it says each player's discards 2 random cards from hand. So what if i draw a weakness. And what if i muligan and redraw this weakness?

You ignore weaknesses during setup. If you draw one as part of your opening hand (even a mulligan), you simply put it aside and draw a new card to replace it.

21 minutes ago, rsdockery said:

You ignore weaknesses during setup. If you draw one as part of your opening hand (even a mulligan), you simply put it aside and draw a new card to replace it.

Well thanks a lot I didn't even know that. But if I wish to keep the weakness in order to maybe discard it can I do it?

You can't keep a weakness that you draw in your starting hand which is created before setup. You can't voluntarily discard a weakness from your hand.

Also, the sentence " And what if i muligan and redraw this weakness? " can't be true, because the cards that you discard when you want to mulligan are not shuffled into the deck until after the mulligan.

Aye, your sequence for this set-up would be:

• Draw opening hand
• Set aside any weaknesses in your opening hand, drawing new cards from the deck to replace them
• Decide on how many cards you wish to mulligan, placing those with any discarded weaknesses
• Set aside any weaknesses from your post-mulligan hand, drawing new cards from the deck to replace them
• Congratulations - you now have your opening hand!
• Shuffle any weaknesses or cards discarded to your mulligan back into the deck
• In the case of this scenario, assuming the correct note is in your campaign log, discard two cards from your hand at random into your discard pile

Assuming you're playing core set only, that should cover everything. Once you start adding cards in from outside core, there may be elements that can change how things go here.