I don't have an iPad, but with iMac and MacBook:
A) to play iTunes audio through proper speakers with airport express
Yes, that will work, iTunes will happily play through an Airport Express.
B) to play BBC Listen Again (via the iPlayer app) and have the sound broadcast through proper speakers, again, via airport express
To the best of my knowledge, that won't work- the only thing that seems able to use the AEX is iTunes. Quite why Apple don't install it as just another sound device is beyond me
There are some amplifiers available that are (or can be) AirPlay capable, Marantz do one that I know of, but whether these would suit your purpose I don't know- I suspect they just "look like" an AEX so iTunes can play to them direct.
If I'm wrong, and someone knows a way to get other applications to play through the AEX I'd love to hear about it...