AC and DC power can flow or exist along the same path/wire, but only AC can pas through a capacitor. The coupling capacitors isolate the DC within the tube/valve while allowing the AC to pass/continue through the circuit.
The filament does not emit electrons. It heats the cathode, which emits negatively charged electrons that are attracted to the B+ plate. The AC signal (from the radio tuning section of the circuit) enters the pre-amp tube via the grid. From the pre-amp tube B+, the AC radio signal passes through a coupling capacitor (which leaves the DC power behind inside the tube) and the AC goes to volume/tone controls. From there, the AC signal in a single ended circuit will go into the power output tube grid. If the circuit is push-pull (two output tubes), there will be a phase inverter tube between the pre-amp and power tubes.