Questions about the first letter of Paul to Timothy. Instead of being addressed to a church, this letter was addressed to Timothy, a convert of Paul's and a pastor (hence, why it's one of the pastoral epistles).
1 Timothy contains counsel to Timothy who has been given charge of the church in Ephesus.
Some of the counsel in 1 Timothy is very specific--Paul had spent multiple years in Ephesus and would therefore have been very familiar with the church and the concerns it faced.
Those who accept Pauline authorship of 1 Timothy have generally held that it was written between Paul's 1st and 2nd Roman imprisonments (circa AD 62-64), though others have proposed earlier dates.
Those who do not accept Pauline authorship generally hold that it was written later in the first century by an anonymous author.