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I gather pilots communicate regularly with air traffic controllers within air traffic controllers' jurisdiction or airspace as they enter the space, during their time in that space and as they leave. In some or most instances, they will not land in that air space, they are simply passing through and may encounter lots and lots of regional and international air traffic.

They are routinely directed by air traffic controllers to fly at a certain direction, increase or decrease altitude for safety in order to avoid collisions and accidents. In most instances, auto pilot is engaged and I assume the headphones come off, for flights longer than say 2 hours or even 1 hour.

Speaker phone may be on but pilots can read a book or watch a movie on their laptop or revise their reading on knowledge of their ever changing craft. At a certain frequency.

I gather lots of communication to planes occurs and listening to all of them can become tedious and may require too much concentration. In this light, do airline pilots ever risk not hearing communication directed to them specifically, from traffic controllers of space they are flying past on cruise?

Does a light or sound or siren switch on when a message is directed at them and I assume they differentiate communication directed at them by their call sign, e.g., American Airlines Flight 200.

Is there a risk they might not hear it and how is that risk mitigated?

There is a ton of radio communication during the taxi, takeoff and departure phases, and then again during the arrival, landing and taxi phases. Pilots are generally very busy at these times and 100% focused. Airlines have two pilots, and one will be flying while the other works the radios and monitors various instruments.

Cruise is another matter. There generally isn't a lot to do other than keep an eye on the autopilot. The pilots will take turns eating, resting, going to the lav, etc. Radio work usually involves little more than getting handed from one frequency to the next. They may get rerouted due to traffic or weather, but it only takes a few seconds to update the autopilot.

Either way, pilots do occasionally miss radio calls. So does ATC for that matter. It's common enough that nobody gets worried about once or twice, though it's annoying. If it's a real radio problem, there are procedures for both sides to follow to keep everyone safe.

There (usually) isn't any sort of light or tone when someone is calling you. However, the standard format is "called station, calling station, message", so with a little training, your brain can quickly tell whether the message is for you. If so, it "tunes in" and you consciously hear the message; if not, it "tunes out" and the message is just background noise.

When a pilot is given instructions, clearances etc. from a controller, the pilot has to acknowledge they've heard it and certain items need to be read back to the controller. If the controller doesn't hear anything they will repeat their message and keep trying to contact the aircraft. The rules for UK readbacks are included in a CAA document CAP413, along with other conventions and standards for communication between flight radio telephony stations

It's not that uncommon, these days, for fighter aircraft to be scrambled to intercept unresponsive aircraft

There is less communication that you'd expect once you've made contact with a controller and been given your clearances. It isn't an onerous task to listen in to all the chat and respond when you hear your callsign

Normally pilots do not communicate much with ATCC between airports. For example, in small aircraft normally the pilot will often hear nothing from ATCC unless they have specifically requested flight following. Small VFR aircraft usually fly with a 1200 transponder code which is generic, and in that case it is tricky for an ATCC to even contact the plane at all.

For larger aircraft, usually a separation is guaranteed from instructions at the beginning of flight and contact is only necessary if something changes, so your guess that they talk to the pilots "regularly" is not really correct.

Note that most commercial aircraft monitor 121.5 in addition to their assigned frequency and an ATCC will always try that if they are getting no response on an assigned frequency. So, big planes have to screw up twice to go incommunicado completely.

If an aircraft is unresponsive, then what happens depends on a lot of different factors. The bigger the aircraft, the more actively ATC will react. If it is a small aircraft on IFR, then ATC will assume the pilot is on the wrong frequency and just steer other aircraft around them. If that causes a big problem, the offending pilot will get written up. Usually the pilot will figure out he is out of contact once he gets closer to civilization. If it is a heavy, ATC will make repeated attempts to contact and do the same thing as with a smaller plane: steer others around them. If the heavy is unresponsive and deviates from its flight plan or remains unresponsive for a long time, then fighter aircraft will be scrambled to intercept and observe them. Obviously, if a commercial crew with a lot of passengers goes unresponsive for so long that it requires an intercept, they are going to get in trouble. By "they" I mean the captain and first officer.