[Mondial]

It seems like the tube is not oscillating. Grids #1 and #2 form a triode oscillator with grid #2 acting as the plate. When oscillating, grid #1 develops a negative bias by rectifying the RF signal generated there by the tuned circuit. If the circuit is not oscillating, the lack of negative bias on grid #1 will cause grid #2 to draw excessive current, which is why the voltage is dropping so low and the resistor is overheating.

Something is wrong with the coil and capacitor which comprise the oscillator tuned circuit. The feedback winding of the coil should return energy from grid #2 ( "the plate" ) to the main tuned circuit in the grid #1 circuit, causing it to oscillate.