1. yes your luggage will be checked all the way to Las Vegas,
how ever, since LAX is your first port of call in the US, you will have to clear customs and immigration and then recheck (hand over ) the bag to AA reps outside of customs etc
2. You will exit customs etc , and again go thru security (internal US) , there are not flight transfer immigration areas, it would apply if you are in transit to another country other then the US

Just to note, if you are on one PNR, AA will protect you if you miss your original flight and put you on another flight to Vegas

3. Hope you come back richer then poorer