Permeability of Plasma Membrane
Passive diffusion.
This question specifically refers to passive diffusion.
Ill reiterate and clarify what was mentioned in the question.
Passive diffusion involves a molecule dissolving into the membrane, diffusing across it, and then dissolves in the aqueous solution on the other side.
The second part of your question can be answered briefly: this diffusion event occurs from time to time, and often at a high rate.

Importantly only small, relatively hydrophobic molecules are able to diffuse across a phospholipid bilayer at significant rates. Thus, gases (such as O2 and CO2), hydrophobic molecules (such as benzene), and small polar but uncharged molecules (such as H2O and ethanol) are able to diffuse across the plasma membrane. Other biological molecules, however, are unable to dissolve in the hydrophobic interior of the phospholipid bilayer. Consequently, larger uncharged polar molecules such as glucose are unable to cross the plasma membrane by passive diffusion, as are charged molecules of any size (including small ions such as H+, Na+, K+, and Cl-).
-Cooper, 2000

Hydrophobic fatty acids repel charge.
The additional or missing electron gives the ion its charge. The hydrophilic head groups of the bilayer are charged, but the fatty acid chains are not, and these repel charge.
There are also repulsive forces between hydrophobic and polar residues (hence the bilayer exists in water), however polarity is essentially a spectrum. A small relatively non-polar polar molecule will not experience enough repulsion to stop diffusion, but a larger, or more polar molecule might.
Active and passive transport.
Although not mentioned in the question, these ions and other molecules can permeate the membrane via protein channels that allow, often with great specificity, ions and large molecules to traverse the membrane.