How does one determine the current draw on a single circuit?
There are a variety of pre-made products which do just that.  The controller sits inside your electrical service panel (or on a single circuit) and you place a "clamp meter" around the hot wire in question.  It then communicates with you via powerline signaling or WiFi (cute little WiFi antenna pokes out of a knockout on your service panel.  

Obligatory warning that nothing about being an electronics guy prepares you for the requirements of mains electrical (and in fact mis-trains you).  One cannot just hack random electronic components into a mains electrical system, even if the components are UL listed.  You may only use approved, preassembled equipment that has been UL* listed as equipment for use with mains power, and you must install it according to its labeling and instructions**.  These items are not found at Mouser electronics, Amazon Marketplace, and damn well not Alibaba.  They are found at big-box retailers (though they can be sloppy) and your local electrical supply house.  You also cannot mix class 1 and low voltage wiring.



* or similar testing lab.  CE is not a testing lab. 

** because the listing is contingent on installation in that manner.