Short answers, pulled from the story.
The problem of other minds asks how one can know that others have minds given that only their behavior can be observed. Knowledge of other minds is always indirect because no one ever sees another person's thoughts or feelings directly.
Solipsism holds that for any person only one's own mind is known to exist under this view. No amount of sophisticated behavior guarantees that thought occurs within another being according to this extreme version of doubt.
Karl Popper proposed a practical test in 1953 to resolve the issue. He published his ideas in Language and the body-mind problem: a restatement of interactionism at the 11th International Congress of Philosophy.
Science offers a different angle through innate mirror neurons which are biological structures supporting the theory of mind mechanism found in humans. Evidence shows that behavior often results from cognition which requires a brain and consciousness frequently accompanies this cognitive process.
Christian List developed a quadrilemma involving four competing claims about consciousness where at least one must be false according to his model. The claims include first-person realism, non-solipsism, non-fragmentation, and one world.