Not quite correct in your explanation of biliary obstruction. If biliary outflow is obstructed, more soluble conjugated bilirubin is excreted into the urine (because it cannot go into the GI tract due to biliary obstruction), causing dark urine. The obstruction prevents excretion of conjugated bilirubin into the GI tract, so less urobilinogen (and later stercobilin) is formed and you get pale stool.

Edit: also, gallbladder obstruction would give you cholecystitis but would not give you symptoms of obstructive jaundice like dark urine or acholic stool

You have to refine your model of what constitutes “pushing” when you consider atomic or subatomic scale. It would be different from the macroscopic view of pushing.

Nothing has to know about the concentration gradient. As long as there is a way to flow, substrates will spontaneously flow.

Substrates flow down their concentration gradients the same way that if you pour concentrated syrup into water, it will naturally spread all throughout. The reason why it does this is that it is thermodynamically favorable to equilibrate like this.