At what point do electrical signals become actually logic and programmable language?
Most your questions are covered by the field of "Switching Circuits" (and more generally, "Circuits and Logic Design", which are both part of computer engineering. 

Try to find a textbook on switching circuits: it will explain how to take transistors and create AND / OR / NOT gates out of them. 
Then find a book on logic design: it will explain how to use AND/OR/NOT gates to build more sophisticated logic primitives such as flip-flops and latches (as well as adders, subtractors, or even a CPU)

Then you will (hopefully) have more insight regarding how the low-level works to realize the high-level ideas.