Is there a transfer desk for US connections airside at T1?

There is but you are not technically connecting, you have two separate flights. So not sure if you can use that desk. In any case, when checking in at LGA the agent will verify you have all the required documentation to enter Canada, because according to your ticket, that's what you will do.

It is not prohibited, but AC will not through check your baggage and will not be responsible for a misconnection.

And I am surprised you actually can save money this way. I always want to do self connection at YYZ with AC for US transcontinental trip but it is usually much more expensive than just flying UA.

How much time are you leaving between both flights? If you are taking a morning flight to YYZ and then an evening flight to SFO (i.e. 8 to 10 hours in between), I would not foresee any issues. If you have like 2 or 3 hours between the flights, AC may judge this as a potential cabotage violation and not let you board in LGA.

When I have done these itineraries before, (including some on the same ticket), I always had more than 4 hours between arriving in Canada and departing to a different point in the USA. YMMV

Transit Question
 

I am flying DXB-YYZ-EWR with a 7 hour layover in YYZ. I am a Canadian citizen and will have checked luggage. Can I exit through Canadian customs and then enter US customs and immigration landside later? In the past this would not have been possible as US baggage was collected as a special/separate carousel (IIRC) but this is no longer the case with baggage being checked through but was not sure if it would cause any issues. Thanks!

Regardless on whether your bag was truly checked through or not, just avoid signage for "connections", especially signage for "US connections" and just find the ones that go to Arrivals/Baggage Claim a.k.a. the very very large immigration hall

Then you're landside :D

CBSA might get a ping on their computers that you have checked bags attached to your reservation but I'm sure you can easily explain that if it comes up. Plus there should be zero issues for a Canadian returning home anyway