The article does note the first point -
Regardless of the year, make or model of vehicle NEVER disconnect the car battery while the engine is running or the ignition key is on.
The alternator has a certain amount of energy in its magnetics, and even though the regulator will switch off when the output voltage rises, there needs to be a path for that energy to dissipate, if it can't go to a low impedance load, ideally the battery, it can generate a damaging spike. Some alternators include protection against this "load dump", and that protection may be elsewhere in the system, but if not, electronics can get damaged by it.
Removing either cable opens the circuit, the negative one is the first you disconnect and the last you disconnect to avoid the risk of a tool shorting between the positive clamp as you fasten it and the bodywork.
The warnings about loss of the memory contents are true, but the ECM has a default set of values which is good enough to start using the vehicle - this is what happens when the vehicle first drives off the production line, so it must be functional to a reasonable degree. It can often take 100 miles or so for the full table of fuel trims to be fully updated, and there's a readiness monitor for emissions testing that requires a number of engine start/warmup cycles before it will report that the emissions system is functioning when it gets plugged into diagnostics for an emissions test.
THe settings that identify different modules to each other are generally in non-volatile memory, and it's not likely that the AC or radio will stop working, though.