As another has said, the antique radio forum is the place to go for this.
Orange orange brown is a 330 ohm resistor, since it's larger it's rated at a couple watts. I can't quite see where it's connected, between ground and something. But R36 on the schematic is a 350 ohm 2 watt resistor, this must be it - value may have changed during manufacture. It'll like get warm during operation. It provides bias by making the cathode more positive than the first grid. The cathode is pin 8 of the 6F6, you count clockwise starting at pin 1 just to the left of the key notch in the socket. You can find pin outs online or in an RCA tube manual.
If it's getting too hot to touch, smoking, or discoloring, it's getting too hot. Verify it's still around 330 ohm (the silver means it's 10% tolerance), it may need to be replaced if it was damaged from the over heating.
At minimum the electrolytic capacitors must be replaced. Likely the source of the hum. Do not be tempted to place new capacitors across the old, the old must be disconnected from the circuit. Since this capacitor is mounted to the chassis, leave it in place for aesthetics with new caps below (some disassemble and hide the new ones inside). Note it's a multi section type with the capacitors sharing a common negative connection. A shorted capacitor could take out an irreplaceable part such as the power transformer.
Next the paper capacitors need to be replaced - these have a high failure rate and leak DC. Many look like paper tubes covered in wax, the one on the volume control needs to be replaced too, it's a bakelite or other plastic package. Use same or exceeding voltage rating. You can find more info on this over at antique radio forum including where to buy replacements. Note you may not find values like .05?F, use modern value .047?F. Back then they called this mfd or mf, same as micro (?) today - pico was mmf then.
I can't quite read the number, but the coupling capacitors between the 6SQ7 plates and the 6F6 grids, if leaky, would put plate voltage on the grid causing excessive current through that resistor.
Check those by disconnecting one end and measuring the resistance. You should see a quick dip in resistance as the capacitor charges then go to infinity, a good capacitor does this almost instantly, second or two. If it doesn't go to infinity or does so slowly, it's leaky. If it checks ok, replace it anyway, it will go bad or is malfunctioning when high voltage is across it. No need to check the actual capacitance, they don't lose capacity, they become leaky.
The output is high impedance, if you connect a (8 ohm) speaker to it, the output will be very low. You'll need a matching transformer. The original matching speaker had this mounted inside.
The manual/schematic doesn't show voltages. You should find a high voltage from ground to the 80's cathode (200 to 350 or so volts), the cathode will be positive - the cathode is the heater on this tube, pin 1 or 4, the thicker pins. High voltage AC on the other two. You'll find high voltages at the plates and screen grids. On the cathodes you'll find zero to a few volts and on the grids zero or a negative value.
This radio does need an antenna to operate - connect several feet of wire to the antenna connection, if working, you'll get local AM stations and some shortwave. Performance will be very good once recapped and re-aligned.
Be careful due to the high voltages.