1) The first thing always to check is whether the op amp has negative feedback from the output to the inverting input.  This circuit has feedback to the non-inverting input, so it shows positive feedback.  Open loop would mean that there was no connection from the output to either of the inputs.

2) The ideal model for the op amp would have no input currents, which implies infinite input impedance.

3) For the ideal model with negative feedback, the voltage difference between the + and - inputs will be virtually zero, and there will be no current in/out from the op amp's inputs.  Thus, vx = 0, v0 = -2V, I1 = (1-0)/5k = 0.2mA, and I2 = zero.

4) Again assuming an ideal op amp model with negative feedback, VA = 0, Vo = (-2 + +4) = +2 volts, I1 = -0.1mA (since vo = 2V and VA=0, current in 20k resistor is I1 = (0-2)/20k), and IL = vo/10k = +0.2 mA.

5) Ideal op amp with negative feedback:  voltage at both op amp inputs is the same, which in this case is zero, and no current into the op amp inputs, so the 4mA must appear in the left 2k resistor.  This puts 8V across that resistor, so the voltage at the middle node is -8 volts.  This means that the current in the bottom 2k resistor is 4mA up, so the current going into the middle node is a total of 8mA from the left and bottom 2k resistors. KCL says that io must be -8 mA.