OK - I don't know your welder - but the basics are essentially the same for most transformer machines so I'll pitch in & maybe kick start some answers for you.
If I understand you correctly the breaker tripping & smoke happen as soon as you switch the machine on - not trying to weld ?
If so you have two issues to figure out - the picture shows the main transformer secondary winding tails going to the rectifier pack & the close up is of one diode - this would mean that the contactor is on & the machine live without operating the torch switch & almost certainly a dead short across the output - hence the angry transformer hum & smoking diode - this may be as simple as a bad torch /connection or more serious - the fact you had smoke from a diode does not bode well - but they can get hot without dying for short periods.
to start I would disconnect the torch from the machine completely & the main DC output leads off the rectifier pack - now switch the machine on - you should have no transformer hum or contactor noise - only the cooling fan if fitted - if it remains on without tripping the breaker bridge the two switch wires to put power on the transformer / rectifier - you should expect depending on voltage setting to have at least 15 volts > maybe 30 volts - if everything is still on try re-connecting the power leads but not the torch - if still on after this inspect the torch / hose assembly & carefully re-connect - hopefully somewhere along the way you've found a bad insulator - damaged wires or something to explain the original problem - if you can figure out a fix try the welder - but it's possible the rectifier pack has been hot enough to damage it - I can't make out in the picture if this means a complete replacement or as on bigger sets the individual diodes can be changed - perhaps you can report back on progress or if you have any specific questions or a picture of any part your unsure of - with luck someone with experience of this model may chime in given time - sometimes it takes a while with time zone differences & working hours.
P.S. Welcome to the forum & good luck with the fix.