Understanding Membrane / Resting Potential from the perspective of ions?
Ah, what a classic biophysics problem.

One first needs to understand how a membrane gets a potential. The lipid bilayer is a large sea of hydrophobic interactions that essentially prevents any ion from crossing. As a result, Na+ and K+ concentrations remain constant and different on the cytoplasmic side and the extracellular side. However, ions can pass through ion channels like the K+ channel. It is important to understand that in K+ channels, only K+ can pass and these channels are actually selective against Na+ (answer to question 1).

There are two potentials at work here. First is a chemical potential created by the flux of K+ from high K+ to low K+. The second is a counteracting membrane potential created by a charge imbalance. Note, that the swapping of a few ions will a) result in a negligible change in the concentration ie. the chemical potential, b) result in a large change in the membrane potential. At some point, the flux out due to the chemical potential and the flux in due to the membrane potential will be equilvant and the cell will reach a resting potential otherwise known at the Nernst potential or equilibrium potential (technically a steady state).

When a cell depolarizes by closing these channels, the local charge will quickly go back to an equilibrium or a non-charged state.

So why K+ rather than Na+? For typical cells, the extracellular concentration of Na+ is 145 mM and cytoplasmic is 12 mM. For K+, it is 4 mM and 155 mM respectively. Doing the appropriate calculations of the Nerst potential, for Na+ it is +67 mV and for K+ it is -98 mV. Qualitatively we can see that this would result in vastly different things.

Most of this information can be found from Pollard and Earnshaw's Cell Biology