Here’s a quick overview.
In terms of the EU legislation on airline compensation, the short answer is that while people affected by strike action are likely to be covered by the compensation rules, people affected by airport strikes aren’t.
The general rule is that if the delay or cancellation is something that the airline could have foreseen (or done something about), then compensation is applicable. This is generally held to include strike action by their own staff. This means that the airline is covered by the compensation rules (even if they don’t like it).
However, if it’s something that’s outside of the airline’s own powers, like the Heathrow ground staff strike or an air traffic control strike, that’s not the airline’s fault and therefore they would not usually have to pay the compensation – though the airlines affected would still have to try and get everyone rebooked as soon as possible.
Even if the strike is called off, lots of holidaymakers are likely to be affected because some airlines will have pre-emptively cancelled flights. This is super annoying, but without all the necessary staff to ensure the smooth turnover of flights, the airlines have little choice.
The airport will likely be open and running, but if a walkout goes ahead, it will add time to things like checking in and security. So if you miss your flight due to not making it to the gate on time, you’ll be out of luck. Passengers should follow their airline’s advice. They generally recommend leaving two hours for short-haul and three for long-haul, especially if you have luggage to check-in.
The simplest advice is to contact the airline and take their advice. They’re obliged to get you where you need to be as soon as possible, but that doesn’t necessarily mean on another airline, so don’t rush out and rebook without speaking to them. You may have to fly from a different airport though. If the time to rebook you is straying in to two days (there’s no definitive timescale for this I’m afraid but two days is a good marker) then it’s reasonable to ask if you can be booked with a competitor.
Connecting flights booked as one purchase are covered – the airline should get you to the final destination regardless. But beware the perils of booking separate legs as if you’ve done this and miss your connection there is no obligation on the airline.
This one is at the airline’s discretion. If you’ve ever seen a latecomer sobbing at the gates, they’re usually out of luck. Though given the circumstances there may be a bit more flexibility. Be nice though – it’s not a legal right.