Hey, not sure what's causing these issues, but it's either (a) network issues again, or (b) the BBC streams (which remember are designed for Symbian, not Android!) have been altered in some way that OpenCore2 isn't exactly compatiuble with. There's not a lot I can do about this unfortunately except say to try again later.
As for download capability, I'd love to add this. At the moment Android only supports OMA DRM 1.0, whereas iPlayer on mobile phones uses OMA DRM 2.0. I *could* have beebPlayer fetch the unencrypted iPhone streams, but this would land me (and the BBC) in a bunch of legal trouble so this isn't a viable option I'm afraid.
But I am aware of both these major issues and am investigating constantly! Sorry to hear you're having problems.