How correct is my understanding of basic electricity?
Some find it easier to understand electronics using physical world metaphors:

Consider the voltage source as a water pump which produces pounds per square inch of pressure.
Consider the wires as pipes.
Consider a resistor as a constriction in the pipe.

At every point between the high pressure side of the water pump and the constriction, the pressure is so many pounds per square inch.  After the constriction the water pressure drops to zero and the water is free to flow back to the water pump.
Note:  Even though all the pressure drops across the restriction, the water still flows!
So, in this metaphor:

The water pressure is the voltage (V).
The water flow is the current (I).
The constriction in the pipe is the resistance (R).

A useful relationship between these is:

V = I x R

...to solve for values other than V just rearrange the equation to suit your needs:

I = V / R
R = V / I

For more on using a Hydraulic Analogy see this Wikipedia.org article.