Explanation of Expressions of the number required of independent equations to analise a circuit
The goal of circuit analysis is to find the currents through and the voltages across all the components.  Ideal sources are a bit special because we don't have rules that relate the voltage the current.  If you solve both KVL and KCL you will get all the voltages and currents.  For KCL one node is a reference so N-1 is correct for the number of equations.  For KVL it is the number of loops that matters.  If using KCL and you have a voltage source you will need to create a super node or write and additional equation to completely solve.  Similarly if using KVL with a current source you you will need and additional equation.  If you are doing this right you will not get an over specified set of equations.  Typically both KCL and KVL are not done.  You can pick the one that is easier depending on the circuit topology.  For example if there is a current source and a bunch of resistors, it will probably be easier to use KCL and avoid the extra equation.  This would give you all the voltages.  Then you would use Ohms law to get the currents.  This saves doing KVL.  



For the I1 loop;

-I1xR1 - V2A + V1 - (I1-I2)xR2 = 0

For the I2 loop;

-(I2-I1)xR2 - V1 -(I2-I3)xR6 - V2 - (I2-I3)xR3 = 0

If you write the equation for I3 and an extra equation for the voltage across the 2A current source that I've labeled V2A in the I1 loop, I'll check back and tell you if I agree.  If you solve these four equations you will know all the currents.  Then you can find the voltages using Ohm's law.  Instead of Ohm's law you could solve the node equations but that would be much more work.