You might be interested in reading the book "I Robot" by Isaac Asimov, which is a collection of short stories examining different variations on this question. But spoiler alert the robot would choose the action that in it's own reasoning would cause the least injury to humans, and if it couldn't stop injury would probably damage it's positronic brain in the process.

Depends on what other choices and freedom of movement the robot has.

It might be able to invoke the third law's exception and give its life to save all the humans. (Are there any on the trolley? That might affect things. It doesn't say one way or the other in the memes.)

Maybe it doesn't have to give its life. It might be strong enough to lift the trolley from the tracks and set it down ensuring anyone on the trolley doesn't come to harm.

But assuming the robot must not leave the spot by the lever and has no non-human-like special abilities, I think the first law has a gaping hole in it. It says it cannot harm a human or through inaction cause a human to come to harm. This means the robot throws the lever, whatever position it was in previously. Because then it has acted.

The fact that other humans come to harm as a result is not the robot's fault, it's the trolley's, and it acted to prevent harm.

If you haven't, read Asimov's works. His main theme is "there is no perfect set of rules for robots", that no matter what there will always be exceptions and loopholes.

Depends on the bias of the programmer or just be random due to the impossibility of making a correct choice. If we haven't been able to solve the problem, a robot will never unless it knows something we dont (in this hypothetical, not an option) or is able to take an action we could not.

It's such an absurd situation that I don't think it is constructive to consider. There are always more options in reality than a binary choice, and likely even more to a machine who could consider so many more inputs so much faster.

In the end, an accident is just that, an accident. No matter how well you consider all possibilities and design contingencies, there is always risk in everything. After an accident, we assess what happened and modify our assumptions about the probability of the event repeating, and make changes to reduce the odds of it happening again.

That said, if someone makes a mistake that leads to the robot switching the track from an empty one to one with people, that's not an accident and someone fucked up royally