Could anyone explain what Counterparty's purpose/future are given Symbiont? What is it planning to do/be that Symbiont isn't planning to do/be?
Symbiont is using the Counterparty protocol to execute its model of "building the first issuance and trading platform for smart securities on blockchain technology." Symbiont will be one of what will eventually be many front ends to Counterparty's back end.
So there's no overlap between what Symbiont is/plans-to-be and what Counterparty is/plans-to-be?
No, beyond the fact that Symbiont is essentially financially backing future Counterparty open source development, by employing most of the core team and enabling them to spend some of their time working on the extant Counterparty codebase. Symbiont is a business with a commercial business model, Counterparty is an open source technology project with no commercial business model. (And yes, the foundation does take donations, but I don't consider that a business model

.)
So, when Symbiont is up and running as a decentralised exchange - it'll be powered by the XCP network? In other words, all Symbiont transactions will run through XCP?
I don't get how that would happen - I understand the transaction-speed/bandwidth(?) of the bitcoin network is too slow to accommodate the demands of the financial markets. Am I something here?
Yes, it will be powered by Counterparty/XCP.
Apparently the founders of Counterparty/Symbiont disagree with your assessment of transaction speed being too slow. Perhaps it's because a clearing house will be built into Symbiont that will allow faster settlement, or something (maybe the Ripple link helps answer your question?). Unfortunately, I don't have a great answer for you.
The Bitcoin network will not have to instantly have the bandwidth to accommodate the entire financial markets right away. It will be a process and its performance can be improved with time. At least that's my understanding of it.