When we start solving the circut, we replace the Current source (I3) with the Voltage source (V3) and we draw three currents going clockwise. But, shouldn't the last current (Iiii) go counterclockwise? Thank you!
But, shouldn't the last current (Iiii) go counterclockwise or it is optional?
If you drew the current one way and the result (after calculation) was a negative current then you know the arrow you drew was the wrong direction. It's a self-revealing thing and nothing to worry about.
In KVL and KCL theorems directions are chosen as the conventional as in your case all are clockwise so that when you go through the loop the current will be taken as 1-2 and which is traditional so as to not create any confusion. And by doing that whatever ans you may get if it had the negative sign then that shows it is reverse direction than what you've assumed. Same case happens for KCL, though we know that current will flow out of the supply but sometimes for convenience we take all currents are going outward from a node.