Notoriety and pickpocketing

Solution 1:

No, pickpocketing is considered an "illegal" action, which will always raise your notoriety. The only reason you were able to do it during Sequence 1 without penalty is because the game's notoriety system had not been introduced yet, so nothing added notoriety.

Honestly, the amount of money you gain from pickpocketing is so small that it isn't even worth doing. Buy a Treasure Map from an Art Merchant and spend some time collecting treasures if you need money right now, but once you progress through the game to the point where you start receiving "income" (won't spoil anything about the source), you should quickly end up with more money than you can ever possibly spend.