Faal moves up four steps of the English football pyramid from the Isthmian League to join the League One side.
The 22-year-old striker, who scored 27 goals in 30 games for Enfield, had been linked with Premier League clubs, including Crystal Palace and Norwich.
Midfielder Hamilton, 21, joins Bolton after his Southend loan was cut short.
The former Scotland Under-19 international, who is yet to feature for Manchester United's first-team, made 18 appearances for the Shrimpers, with his last game for Sol Campbell's side coming on 7 December.
Wanderers have also signed 18-year-old midfielder George Thomason from ninth-tier Longbridge Town.