There are people far more qualified than I here to answer this, but since none seem to be around, I'll throw a dart.

1) I don't think it matters if you can check it through or not, since [I think] you'll need to collect your baggage and clear U.S. customs in LAX (though I'm not sure how the whole U.S. border preclearance thing affects this, if it's even offered YVR-LAX--and AFAIK, it's not considered a domestic flight). Whether you'll be able to immediately drop your bags off at CX or not is another issue--AS's rule is not earlier than 4 hours before flight, but CX might be different.

2) AFAIK, anything more than 4 hours is generally considered a stopover. I'm not 100% sure this is consistent across airlines, and I have no idea how this affects bags, especially on separate tickets.

I'm sure someone more knowledgeable will be along shortly to correct me, but I hope this helps.