Sad to say, the BBC is a pale shadow of what it once was. Their services have been drastically cut back over the last few years.
There are many different sites with online schedule information - but you have to watch, because not all of them update their info in a timely manner. Schedules change frequently these days (used to be that the schedules would undergo major changes twice a year. Not anymore....). There are several of these listed in our wiki here (see section 7)
SWL Broadcast - The RadioReference Wiki
There is a Yahoo group that has a spreadsheet that incorporates these sites and many more...
https://groups.yahoo.com/neo/groups/swskeds/info
Finally, the DXLD Yahoo group run by Glenn Hauser has probably the most up-to-date listing of schedule changes anywhere, bar none...
https://groups.yahoo.com/neo/groups/dxld/info
Now onto the bigger question - HF has many different types of broadcaster, everything from the huge powerhouses (which are gradually dying out), local broadcasters, hams, CBers, and the catch-all category known as utilities - which is pretty much anything else. Yes there are some military stuff here, but you will never ever hear the good stuff, which is often encrypted and sent out on secure means. Since you mentioned it, aviation has a very large presence here, both with voice and digital (which you can decode with software, some of it free)
But before you get into that, you need to understand how a signal gets from point a to you. The topic is known as propagation, and there's an excellent website (requires Flash player, by the way) that will give you a start in understanding this topic
Propagation Primer - Flash Movie by AE4RV
This can be a very complex topic - we don't understand it all yet- but you don't need to have a degree just to get the basics.
Enough for now, I think - I'm sure you have more questions, fire away...Mike