Engine shut off whit no warnig light

SOURCE: P0505 Code

First make sure that your wires to you iac(idle air control) motor are ok. Also that the pins in the connectors are not damaged. Most likeley you need to replace the iac motor and follow a relearn procedure for the pcm.(powertrain control module)
The iac is most likely stuck in the extented position causing it to starve for air. You have to hold your foot on the gas to keep the throttle plate open enough to let air by for the engine to run.

SOURCE: how do i reset my check engine soon light 2005

you can buy a code reader from an auto parts store that will give you the ability to reset the check engine light, or most parts stores have one that they use on customers cars at no charge. if you ask them to read which code your car is throwing, most of them will let you hit the button to clear the code. they aren't supposed to do it themselves for some reason, but from my experience they will let you.

SOURCE: 2003 nissan murano with check engine light codes

P0420 is Catalyst System Efficiency Below Threshold - Bank 1
and
P0456 is EVAP Control System Very Small Leak (Negative Pressure Check)