Welcome to the SQ Forum.. Please look at the other threads for SIN-EWR-SIN and SIN-LAX-SIN
These flights are indeed nonstop on an Airbus A340-500 which is designed for this long haul service. The number of seats are reduced in Economy providing for 117 seats and 64 raffles (business seats). The economy seats are more spacious than other SQ aircraft.
To be applicable to your travel, there is nonstop service from LAX-SIN (and SIN-LAX) nonstop with the same A340-500 aircraft preventing the need to stop in Taipei , Tokyo , Hong Kong or Seoul.
(See:
http://img.singaporeair.com/images/e...s/A345-500.gif )
Also some pictures of one of the aircraft:
http://www.airliners.net/search/phot...nct_entry=true