Sounds like a bad heater core is causing all your coolant system problems. That will give you what you are describing and causing the cold air but hot engine issue. Basically, it sounds like you are so low on coolant (because of the heater core leaking) that there is not enough coolant to heat the core to give heat into the cabin.
Fix that and don't drive until you do. That or disconnect the heater core from your coolant system. Either way, you should not be driving a car with cooling system issues.
To disconnect/bypass the core, there should be 2 pipes that come from the engine that go through the firewall and into the cabin. Those are the "To" and "from" pipes to your heater core. You can just route a hose from one engine side connection to the other (make sure you route the hose to the connections that are on the engine!). But you won't have heat this way (you are bypassing the core by doing this).
As for the copper in the system, could that be from an additive to help stop leaks? Maybe previous owner tried this to stop the heater core leak? I would flush that stuff out though...i have heard it to cause other issues.
As for the slowness, I am not sure. My 95 318ic is suffering from the same thing. But we are both coming from forced induction so it's a bad comparison!
Good luck! Looks like a nice car!