Yes, YEG is one of the airports where pre-clearance is available:
http://www.cbp.gov/xp/cgov/toolbox/c..._locations.xml
There is no easy answer to your last query. They can ask for your return ticket if they doubt your story! Bank statements, not so much. Here is what I expect:
Q - Citizenship?
A- Canadian.
Q- Where are you going?
A- LAX?
Q- What is purpose of your visit?
A- Vacation.
Q- What are you bringing that you intend to leave in the US?
A - Nothing.
Have a good day!