Is what the Shaykh mentioned correct, that it is impossible to completely stop committing a specific sin, citing that humans are weak and fallible, and that a believer might commit adultery and steal?

Faith does not mean infallibility from sins; for all human beings are inherently prone to error, as Allah Almighty said: "Indeed, he was ever unjust and ignorant." This does not mean that every believer commits heinous sins; rather, sins are of various types, including neglecting obligations and innovations, not just the well-known heinous sins. A Muslim must hasten to repent from sin with its conditions (abstaining, regretting, and resolving not to return to it), and not use the lack of infallibility as a pretext for persisting in sins.