Is it permissible to inquire about the character of a man whose reputation has been tarnished due to the words of three people, knowing that the questioner has not seen or heard anything from him, and this man associates with a close friend of the questioner?

One must think well of people and interpret their actions in the best possible light, unless there are indications or evidence to the contrary. If those who slander the man are known for their religiosity and truthfulness, and have no personal interest in accusing him, then it is permissible to believe them and warn your friend about him, for "religion is sincerity (or good counsel)." However, if they are not known for their religiosity and have a personal interest in accusing him, then do not listen to them and do not warn your friend, because that would be following suspicion, which is forbidden by the Almighty's saying: "O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin. And do not spy."