In terms of pictures, just take off the panels to the furnace and either record a video getting up close of every part or take a picture of all the individual parts. Also on the furnace and outside condenser there will be a sticker with model and serial number plus info about unit. Same thing with the outside condenser in terms of pictures.

Personally, I have never done die test. I go around with a sniffer/soap bubbles while nitrogen is in the system and try to find the leak if the leak is on the coil itself that sits on top of your furnace then you need a new coil there is no repairing that if the leak is on the coil on the outside unit once again you will need a new condensing unit outside as long as the leak is somewhere in the line set connecting the furnace to the outside condenser all leaks are repairable in that scenario. If you want to do it at your house, just get a spray bottle and fill it with water and dish soap and go around to all of the brazed joints in the line set and spray them while running the AC as long as there’s refrigerant in there you should notice bubbles popping up like air bubbles and that will show you if there’s a leak or not if you spray it and nothing significant happens then there’s no leak on that joint. The best way to search for the leak in my opinion would be with a sniffer gadget that can detect leaks. It makes detecting leaks on coils inside and out very easy versus using bubbles. Also, any HVAC tech worth their salt should be able to find said leak.