Your assertions are correct. I don't know of a resource for simply decoding all of the airlines' booking codes.

Agents would normally simply look for L class if that's the ticket you have. Seats are normally realised in "ascending" class so if L doesn't have any, none of those below it will (although strange things sometimes happen).

Yes it is possible that some flights never have L class. LHR-GIG does indeed look like one of them, but on some airlines you can get a seat by waitilisting. And sometimes seats get released at the last minute - I can currently see 1 L seat on BA247 LHR-GIG tomorrow - but it would be high risk planning on that basis. You can ticket the segment as open-dated (although not if this is the first international segment) and then if there's an empty seat at check-in most airlines would take you, but BA is a very strange carrier these days, so they might not.

Note that the term "transit stopover" is wrong. You either have a "transit" (less than 24 hours between arrival and departure) or a "stopover" (more than 24 hours). To do what you suggest requires you to have a transit in North America.

Hope that helps.