both of those things are normal, but the CEL should stay on after the engine dies and let you pull the code. If you have the light on and its really not letting you pull the code with a scan tool, there is some sort of problem going on with your scan tool, harness, or the ecu itself.
try using the scan tool again with the key in different positions. Some cars it wont link up if they are not turned to accessory or on.

 

Ok thanks, I'll try that.