Justus and Crispus

After "he departed from" (Acts 18:7) the synagogue, how far did Paul have to go?
Just "next door to the synagogue," to the house of "house of a certain mane named Justus, one who worshiped God" (Acts 18:7).

Who among others followed Paul out of the synagogue to Justus' house?
"Crispus, the rule of the synagogue" (Acts 18:8). Christians should never exclude anyone as being beyond the Lord's reach through our witnessing.

Why did the Lord speak to "Paul in the night by a vision" (Acts 18:9)?
Apparently, Paul had been "afraid" (Acts 18:9), either keeping or considering keeping "silent" (Acts 18:9), and concerned about his safety. It is possible that he had received or heard of threats and begun to wonder if the Lord wanted him to move elsewhere.

Who are the "many people in this city" (Acts 18:10) God mentioned to Paul?
Had they been Christians already known to Paul, the Lord would not have mentioned them to Paul. They were unlikely to have been Christians unknown to Paul since Paul was the instrument the Lord was using to preach the Gospel in Corinth; they were most likely the people the Lord intended to soon convert.

How long did Paul remain in Corinth to teach "the word of God among them" (Acts 18:11)?
"A year and six months" (Acts 18:11)