Effects of a Resistor
Your question is far from clear to me. Your first schematic doesn't even show an LED. I will try to explain how everything works without any mysticism.

Resistors have two terminals, and they enforce a rule between those two terminals.

The rule is called "Ohm's law." Mathematically, the rule is V = I * R.

V is the voltage across the resistor.
I is the current flowing through the resistor.
R is the characteristic value of the resistor, normally measured in units called "Ohm's." Your resistors are 1k, so V = I * 1000.

Diodes are more complicated, so I am going to give you a simplified model. Assuming voltage polarity on the diode is correct (forward bias) the rule enforced by the diode is approximately V = K. (K is a constant). However, if the circuit is not capable of supplying that voltage across the diode, then it will enforce a different rule: I = 0. The constant, K, depends on the type of diode.

For an LED, any time I > 0, it may be emitting light. Red LED's are especially sensitive, and will emit light when even a tiny current is flowing.

A voltage supply also enforces the rule V = constant, normally by supplying current from its + terminal.

You put all these rules together, and hopefully everything will make sense. What circuits do is find the one unique solution to all the various rules. Sometimes the solution conditions cause the diode current (and light) to be zero. One way to check is to remove the diode from the circuit, then solve it. If V where the diode is supposed to go is > K for that diode, then the diode is in forward bias, and you need to put it back in and solve for the circuit assuming the voltage at that node is K.

Hope this makes some sense.