I think it would be a good idea to slow down a little bit. When you have an issue with the amp, the first step absolutely is a set of voltage checks.
The volume going up to maximum would be the volume pot losing its ground connection, which is most often a soldering issue. If the lugs have been squeezed on where they mount to the pot wafer, then replacement will be in order.
The operation or lack of operation of the LEDs on the socket depends a whole lot on what the actual DC voltages are, and resoldering/poking at the LEDs because they don't light up is usually only going to damage the LED itself.
I have never, ever in my 25 years of doing this seen a tube destroy a volume pot in the manner you describe. That doesn't mean it couldn't happen, but this is incredibly unlikely.
On the headphone jack, the tip will not push the spring contact up all the way, but if you are getting sound out of the left channel, it's pushed up enough.