Why put a resistor in series with the positive terminal in a non inverting op-amp circuit

If you do that the amplifier will amplifiy its own output and the ouput will go high or low and stick there until a sufficiently low or high input is presented, which will make it go the other way (low or high).

In essence you will have created a schmitt trigger.

What the formulas don't show is that the solution for this amplifier configuration describes the metastable point,

Another limitation of those equations is that they don't represent the limited output voltage range of real amplifiers.

The non inverting amplifier setup they are describing looks like this:

^{simulate this circuit – Schematic created using CircuitLab}

You need to calculate the value of R3.

When they talk about "what range of outputs would you expect", they are talking about the output with V1 == 0V. That is not 100% clear in the problem description.

So given that, you should be able to calculate the output offset voltage from the bias and offset currents (assume different signs of the offset to get a range). The rest of the problem should be self-explanatory.