AC at LGA should be able to check you in for both the AC and the CX flight even on the seperate tickets (present them both!). A seperate check-in shouldn't be required.

Don't know about the bags. They should be checked through to HKG and moved from AC to CX. There's a pretty good chance that you won't even see the bags at YYZ.

As for T1 to T3, its just a short bus ride.