Who is the believer who carried 1^st Peter to the various churches?

The Believer is Silvanus who helped many times in the early church.

Source: 1^st Peter 5:12

Where was Dionysis the Areopagite converted to Christ?

He was converted in Athens Greece he heard Paul’s sermon and believed.

Source: Acts 17:34

After becoming a Christian this “seller of purple” offered Paul hospitality?

This is Lydia of Thyatira. Possibly the first convert in Europe.

Source: Acts 8:14-15

This early believer was converted by Phillip on his way home, who is he?

He was the Ethiopian eunuch in charge of the treasure of Queen Candace.

Source: Acts 8:27-39

This believer became the Bishop of Crete, who is he?

This is Titus. One of Paul’s disciples he never saw Jesus that we know of.

Source: Titus 1:4-5