The resting membrane potential is close to the equilibrium potential of K+ because K+ is actively placed inside the cell by the ATPase pumps. If there were no ATPase pumps, cells would become more positive and closer to Na+'s equilibrium potential. So, yes, Na+/K+/ATPase pumps are responsible for creating the K+ concentrations that lead to diffusion of K+ in such a way that the resting membrane potential is negative as well as creating a Na+ gradient that allows for quick diffusion into the cell when appropriate ion channels are opened.
K+ rushes out of the cell at rest because K+ channels are open at rest while sodium channels are closed. Not because K+ is just better at diffusing. These are passive channels, not active pumps.
I know hyperkalemia is excess K+ in extracellular fluid. However, if there's a higher concentration of K+ outside the cell, there will be less diffusion of K+ from the INSIDE of the cell to the OUTSIDE of the cell. Less diffusion outwards means more K+ inside the cell then normal because it is not diffusing outwardly as fast.
What you're saying doesn't really make sense. You said hyperkalemia lowers membrane potential (I guess that means more negative) and then right after you say it makes the membrane potential more positive. Which one is it?
Also, can you explain the mechanism behind hyperkalemia making a cell more positive if what I described is wrong?