1. Actually the UK and Canada have a greater population than the US. Let alone the whole empire.
The UK had a population of 29 million. Canada had a population of 3 million. Combined that's 32 million as opposed to the US 31 million; which is not a massive advantage, especially since the UK forces have to cross an ocean.
There is, of course, the rest of the British Empire. Major sections of the empire, such as India, required continued British troop presence, and thus reduced the number of British troops that could be used for overseas actions.
2. The US is massively behind the UK in industrialisation. Worse almost all the US war industries are located with the range of naval artillery. Even worse the US is dependent on the UK for gunpowder and iron.
The British had a blue water, not a brown water navy. While the majority of US industry was near water, much of the rivers and harbors lacked the necessary depth for British warships to sail into them, and sailing against the current with highly restricted maneuvering would not be done lightly. HMS Warrior, for example, had enough draft it could not use the British port of Bermuda.
I'm well aware that the US imported some iron and gunpowder from Britain. Britain also imported some grain from the US. That doesn't mean either was dependent on the other.
3. Steamships make UK logistics trivial, whereas overland transport in the US make things quite difficult.
Steamships do not make logistics trivial, they add to the amount of logistics required. The US was connected to Canada by the
Grand Trunk Railroad, which would greatly aid US logistics.
5. How is the US going to "arm Ireland". More importantly, why give arms to your enemies? The Irish have no love for the intolerance of the US.
The Irish hated English intolerance worse, as after the Potato Famine the majority of Irish emmigrants went to the US, not England. The US arming Ireland is wildly unlikely, a far better use of US resources would be commerce raiding against British shipping.