Being an analog component, a capacitor's capacity to retain a value would not be measured in bits, would it?

Read/write floating point values! Also, design for leakage. ;-)

A transistor is of course also an analog component.

That's pretty much how MLC FLASH works.

Yes - I think that is what DRAM is at its core - and requires more refresh to keep the charge on that capacitor - versus SRAM which is a more complex latch transistor based approach (which also happens to be faster and less power intensive - but also more expensive per bit).

Yes, but that's different.

A simple capacitor does not require an external power supply to store the state, but the state decays in time.

A flip-flop requires an external supply to store the state, but the state is stable indefinitely.

but a well designed CMOS based flip-flop (no resistors) has virtually no leakage current while the sense operation for refreshing DRAM uses a lot

So is a rock.