Very good question. Most of your arguments, to the best of my knowledge are accurate. As to answer your questions, I'll provide a basic model of understanding. (Disclaimer:- I'm sorry if the explanation seems overly-messed up and confusing)
At any moment, the potential difference across the cell membrane has to be such that it makes all fluxes balanced. Let us assume there is a cell with nothing but potassium and non-diffusible negative porteins. Since potassium is the only ion that can have a flux, the only balanced position will be the one with zero flux, because any net ionic movement will cause a change of potential and hence will not be the balanced state. Zero flux will be reached when the concentration ratio of potassium outside and inside is such that the potential difference is equal to potassium's Nernst potential.
To complicate it, let's add sodium. Now the balanced state should have zero net flux. But this does not mean that the fluxes of both the ions is zero. They can be equal and opposite. Let us assume that the permeability of the membrane is equal for both. Then, the balanced potential would be equidistant from the Nernst potential of both the ions. This is because, permeability, in an abstract way, is a measure of the resistance. Flux is the potential difference (between the Nernst potential, where the flux would be zero, and the membrane potential) divided by the resistance (like a simple current), which would be equal only if this difference is same, which is, for a membrane potential midway between their Nernst potentials. Hence, the ion which has a higher permeability, will have a lesser resistance, and would hence require the potential difference to be low, so that the ratio of $PD$ and $R$ be equal to the other ion with a large $PD$ and a high $R$ (low permeability). This $PD$, is not the membrane potential but the difference between this potential and the Nernst potential.
Now, for your first question
...resting membrane potential is reached from the hyper polarised state....
This is simple to understand because the opening of the potassium channels which caused the potential drop to $-90$ has now been reset and the permeabilities have been reset to the original resting values. Since the balanced state depends on the permebilities only, the balanced state of this is the RMP ($-60$), which the cell will achieve. Since $-90$ is unbalanced, the slightly unbalanced flux will cause a drift of the potential towards $-60$ and when it reaches it, the fluxes will match and hence won't deviate any further. The drift is because more of one ion is moving than the other, causing a net movement of charges across the membrane.
.... action of the sodium potassium pumps comes into this....
This is easy to understand but tough to compute. Since the sodium potassium pump is unbalanced, (it puts out 3 sodiums and takes in 2 potassiums), it contributes a net flux always. Hence, the remaining channels, instead of having exactly equal sodium potassium fluxes, will have to have a slight potassium excess to offset the minor flux contributed by the pump. As a result, the effect can be computed in two ways.
We find the net flux contribution of the pump. Now we know by what amount should the potassium flux be greater than the sodium in the remainign channels which follow the PD/R formula and hence we can caluclate the PD such that the fluxes have a certain difference (equal to the flux contributed by the pump)
We perform experiments and directly find a net amount of potential "correction" which has to be added to the potential calculated by matching fluxes because of the pump, which will remarkably stay constant. This method is easier and the value of the correction can be obtained from literature online.
Hope this helped. Feel free to ask for clarifications. If you want net links or references, ask. :)