Some surge protectors work by "redirecting" surges to the equipment ground, which is pretty much the definition of a ground fault. In this case, it's definitely possible that surge suppressors could be tripping GFCI receptacles/breakers (given a large enough surge).
As for the AFCIs... When electrical contacts separate, they often create an arc between the contacts. This arc spans the gap until the contacts are too far apart, and the arc can no longer be sustained. It's possible (in theory) that the GFCI tripping could create a large enough arc, for long enough to cause the AFCI to trip. It's not likely that a properly functioning GFCI would do this, but if the GFCI was old and worn it could be opening the contacts slow enough that a detectable arc is being produced.
Determining if the GFCI tripping is causing the AFCI to trip, is a simple test. Simply press the test button on the GFCI. If the AFCI trips, you'll have figured out half the problem. If the ACFI does not trip, you could repeat the test using a receptacle tester with a GFCI test function.
If it's determined that the GFCI is causing the AFCI breaker to trip, replacing the GFCI receptacle may resolve that part of the issue.
Figuring out if the surge suppressor is tripping the GFCI, is a more difficult proposition. It will likely require you to monitor the supply voltage over some time, to identify and document possible surges.
Arc-Fault Circuit Interrupter (AFCI)
An arc-fault circuit interruption device is designed to detect dangerous arcing within the protected circuit, and open (turn off) the circuit to prevent damage caused by the arcing. It does this using special circuitry to analyse the electrical characteristics of the circuit, looking for characteristics that match specific pre-programmed values. If the AFCI detects suspicious goings on, it opens the circuit.
AFCI breakers are typically combination devices, meaning they also provide similar overcurrent and short-circuit protection to a standard breaker.
Installing a combination AFCI breaker on a circuit containing knob and tube wiring would be a great idea, and could potentially prevent a fire.
Ground-Fault Circuit Interrupter (GFCI)
Ground-fault circuit interruption devices are designed to detect ground-faults, and open (turn off) the circuit when a ground-fault is detected. They work by using a current transformer (CT) to detect current imbalances between the ungrounded (hot), and grounded (neutral) conductors of a circuit. This blog entry might help you understand how GFCI devices work.
GFCI breakers are typically combination devices, meaning they also provide similar overcurrent and short-circuit protection to a standard breaker.
Installing a GFCI breaker on a circuit containing knob and tube wiring, probably won't provide any benefit. GFCI devices are designed to prevent electrocution, not to protect the wiring.
Combination AFCI GFCI Circuit Breakers
Circuit breakers that provide AFCI, GFCI, overload, and overcurrent protection are becoming more widely available. If you can find them for your panel (and afford therm), these would be the best option.
Best Answer
It's probably a good idea for both. A GFCI measures the difference between current into a circuit on the live wire and current out of it on the neutral; the ground wire just helps to make sure that in an electrical fault, the current isn't passing through you to ground. So a GFCI would be good in the places that current code calls for them: kitchens, bathrooms and outdoor circuits.
Same for the AFCIs: they help detect faults due to damaged wiring. With BX cable, that damage is less likely to be caused by driving a nail or screw through the cable than it might be with NM cable, but you still have the possibility of loose connections in your receptacles, or damage to electrical cords going to your appliances.
Another thing to consider: if you have older wiring, you may also have older breakers. If you're replacing some of them with GFCIs or AFCIs, you might think about having the rest of them replaced with newer breakers.