Hi John
My sister has the Stream 93i so I know it reasonably well. Yes, it’s a bit frustrating but you can listen to all the BBC programmes and podcasts which, unfortunately, is not the case with the BB1 (which I have) and presumably the BB2 (which I don’t).
Specifically, in reply to your questions:
No - BB1 cannot access the BBC ‘s recorded shows/podcasts (the 93i presumably accesses these from BBC Sounds)
No - BB1 cannot pause live radio or “remember where you got to”
No - BB1 does not allow you to “navigate to somewhere in the programme”
Also, the 93i allows a wide range of tailoring to the (excellent) sound quality by selecting from a sub menu plus or minus numbered settings for bass and treble (-6 to +6?). The BB1 only offers 5 “Tone Presets” which, frankly, are indistinguishable.
Hope this helps
Jim