Circuit with dependent source confusion
If \$k = R\$ then the voltage across the dependent source is \$Ri\$. The voltage across the resistor is equal to \$Ri\$. You are correct that KVL and KCL will be satisfied for all values of \$i\$, but that does not mean that you can assume \$i = 0\$.

I think you are being asked to think about the value of \$i'\$ as a function of \$i\$, not as an absolute value. You are almost there.