Ok, so I think I've found the answer to (1) above. From within SOPC Builder, the 'Tools' menu allows me to launch Eclipse, and from there I can select 'File => New Application and BSP from Template', which results in a 'software' directory containing (amongst a lot of other things) the aforementioned 'altera_avalon_dma_regs.h' file.
So far, so great. Still not sure what I have to do to get my own component to show up there, though. If someone could point me at the correct documentation, I'd be very grateful :) To a complete newbie such as myself, there's a lot to take in and learn...
Cheers
Simon