Just to clarify a few points about Visual Approaches in the U.S.;
ATC may clear an aircraft for a Visual Approach if the aircraft has the airport, OR the preceeding aircraft in sight. (plus appropriate WX minimums as previously stated.)
ATC is still responsible for IFR separation, EXCEPT that if the pilot has the preceeding aircraft, or another aircraft in sight, and is instructed to maintain visual separation or follow that other aircraft, then the pilot/crew has assumed separation responsibility for THAT situation only. ATC still assumes responsibility for other IFR aircraft not seen by the crew. Controllers are supposed to "Advise an overtaking aircraft of the distance to the preceding aircraft and speed difference."
ATC may conduct simultaneous visual approaches to parallel runways separated by more than 4300', or converging runways, so long as crew is advised such operations are in effect. (usually thru ATIS.) Note, when simultaneous visual approaches are used, only ONE aircraft need be on a visual, the one 4500' off his/her right wing may be on an ILS...
Simultaneous operations to parallel runways separated by LESS than 4300' are approved with a few more restrictions.
Depending on the operation and type airspace involved, the ONLY radar separation from VFR traffic may be target resolution/500'/visual separation. The Tower may be working VFR pattern traffic not sequenced by approach control.