I have a Burham boiler too. Same exact problem was nothing more than electrode adjustment. Every so often, it would ignite & shake the house with a "POOF"!
That burner is on a hinge, One bolt removed, & it will swing to the left -- as long as you have a flexible oil line connected. If not, shut oil off at tank & remove the line. There is a specific adjustment with regards to how far ahead of the nozzle they extend, their height above the nozzle & their gap. I was trying to find the specs for you, but I believe they were left on my virus-filled paperweight of a computer that was just replaced. I believe you can get the specs on Burham's website.
Also check & make sure the coil is making a good contact to the electrodes.
I highly doubt that burnt paint is the result of gasket leakage ... looks to me as if somebody left the burner swung outward for maintenance ... and forgot to turn off the breaker! That will scare the crap out of ya!
As far as the buzzing goes, those aquastats are notorious for that. My parents had one that buzzed for years before they replaced it. Mine was doing the same thing. I replaced mine with a digital unit (forgot model #), just for more flexibility of adjustment. Was still working fine.