They should be able to check your bags through from MIA to BKK all the way, and give you boarding passes all the way through, even if your AA/CX segments are on different tickets.

HOWEVER, don't do OLCI for CX or some AAgents won't be able to print out your CX BPs.

The way it works in Toronto is that after you clear Canadian immigration in T3, you need to collect your bags (which are already tagged to BKK) and then drop them off at the transfer belt (make sure you follow the sign to the transfer belt and don't just walk out into main arrivals hall).

Since you're CX Silver and therefore have a lounge entitlement in YYZ/HKG, I recommend that after you drop your bags off at the transfer belt, you go up to CX checkin and get your AA issued BPs swapped for CX issued BPs and they'll give you the lounge passes for YYZ/HKG as well. This extra process will take 3 or 4 minutes tops and may save you hassle later, or if you're lucky even score you an op-up if the flight is full and the agent is in a fix and needs to release a seat.