dependent current source polarity
The marked polarity for \$v\$ on the current source is the assumed polarity. When setting up a circuit for analysis we may not know the actual polarity of the voltage, so we just make an assumption that lets us write the equations.
If we solve the equations and the value of the assumed voltage is negative it just means that the polarity of the actual voltage is the opposite of the polarity of the assumed voltage. There is nothing wrong with this, voltages can have a positive or negative value.