Welcome to Flyertalk, and welcome to the BA forum.

For the first one, ideally you ring the contact centre as soon as you can to get you offloaded from the service before you can be deemed a no-show. This keeps the ticket "alive". If it's LHR, LGW or JFK you can still see if the staff there will show mercy and rebook you on to the next flight, perhaps charging a nominal £60/$100 as a service fee, but that's not guaranteed and if you are in any way unpleasant about the situation then you will be invited to go online and buy a new ticket. At outstations without ticketing options you are most likely to be referred to the contact centres (though in reality they can rebook you).

Airside, again you ideally get an agent to offload you so the ticket is still kept alive, but if the flight departed without you then you are a no-show and that's it.

I've managed a fairly busy travel schedule where this has never happened to me, other than connections being missed (and to which a different logic applies). So I'm reporting from observation and from FT posts rather than personal experience.