Method of superposition
No, this is not correct for \$I_{11}\$. You combined a number of resistors along the way. Remember that when you combine two resistors in parallel that you lose information about the current through either of the two individual resistors. Likewise, when you combine resistors in series you lose information about the voltage across the individual resistors.
The current you solved for is the current from \$E_1\$ through \$R_1\$. You need to take this information and work your way back to the original circuit to find the current through \$R_P\$.