The gfci function is actually pretty easy to create. Both conductors are passed through a single toroid pickup coil. If the currents are equal the toroid has no induced voltage (the magnetic fields cancel) and nothing happens. If the fields do NOT cancel a triac is used to open the circuit. The sensitivity is as simple as how many turns on the toroid the sense winding has. More turns, more sensitive (less current imbalance). AFCI devices look for the high frequency noise generated by an arc. It will be at a multiple of 60 Hz, so filtering is not that hard. You need to consider that an arc generates electrical noise form the frequency of the voltage to light (the arc itself). The noise twice a cycle as the arc starts and stops with the 60 Hz voltage. Sense the noise, turn off the circuit. AFCI devices are not required to be as sensitive to current imbalances GFCI devices. Arcs do not trip a CB since the current does not exceed the CB rating. An arc from a break in the hot line is going to the hot line. TThe load on the circuit limits the currents, but the arc produces very high temperatures. A fault is when the hot shorts to the neutral (or ground) and the current exceeds the CB rating. Breakers for residential use are thermal-magnetic. The thermal is from heating of a section of conductor in the CB. This allows brief overloads to pass without tripping the CB (like 'slo-blo fuses). A motor starting or heating elemt turning on are allowed to operate since the current falls quickly and fails to trip the thermal overload. The magnetic occurs for 200%+ current and results in a very fast operation. The higher the current the more magnetic force is generated and the faster the breaker opens. At very high overloads the breaker opens in just a few milliseconds. People are not very good conductors. You are very unlikely to ever pull enough current through your body to trip the breaker.

If the wire nuts were melted, the iron certainly isn't your problem. That particular junction that melted was creating heat - and lots of it. Not everything that creates heat will trip an AFCI - and your iron is a good example. The AFCI is measuring current wave forms and comparing it to "normal" waveforms (like turning on a light or plugging something into an outlet.) If the wave form exceeds the normal in speed and intensity, it trips the breaker. The thing that causes heat is a combination of current and resistance. That could be in the form of the resistance of air (as in an arc) or gunk. Or it could be from higher current flowing through a wire that wasn't designed to handle it (as in a bulb too big for a fixture.) Also, ACFI's break. Have they checked to see if it is actually working?

As previous pointed out, when AFCI was added to the code, it's never been a receptacle only thing. In the 2002 NEC, all 15 and 20A 120V branch circuits serving outlets (of whatever nature, lights, receptacles, etc...) in bedrooms was to be protected. In NEC 2005 this was changed to require them to be the "combination" type. In NEC 2008 the areas requiring AFCI was expanded to just about all living space that wasn't required to be protected by GFCI (the wording is specifically "family rooms, dining rooms, living rooms, parlors, libraries, dens, bedrooms, sunrooms, recreation rooms, closets, hallways, or similar rooms or areas "). Of course, you're always at the potential whim of the AHJ on what constitutes enough of a change to require updating to the current codes. It also, depending on the jurisdiciton, may lead to local code differences from the published NEC and give some discretion to the inspectors.

Number of reasons for tripping can be numerous. Better is to learn more about the tripping. Ie determine what must be on to cause tripping OR what, when powered on, causes that tripping. If a motorized appliance causes 'nuisance' tripping, then the appliance has a defect. Some appliance power switches can be designed wrong to cause arcing. Or a needed snubber circuit was eliminated to 'save money'. No way around this. If any appliance causes 'nuisance' tripping, then a defect exists in that appliance. One example of a trip is when the safety ground and neutral wire are shorted somewhere (ie inside the appliance or in wall receptacles). Simply separating safety ground from neutral wires can sometimes eliminate a 'nuisance' trip (that is actually detecting a defect). Another example is a tool that connects a 33K half watt resistor or two 15K half watt resistors (in series) from the hot prong to earth ground (install them inside an AC plug to create a testing tool). The tool should cause no tripping. Then power other appliances. If those other appliances cause an arc or ground fault breaker to trip, then that appliance is leaking excessive current. The defective appliance is not leaking enough to always trip a breaker. The least likely suspect is a defective breaker.