Yes, terminology - it's quite important to get this right as it often leads to misdirection and confusion. I thought you yourself were thinking that the signal had an 'input and output' when this is not the case.
The circuit might have an input and an output - depends on how it's configured* -...
What 'input'. You have a LOAD connected across your FG output and the load has RLC elements and will invariably affect the FG output in the way shown.
It's not as if the rising edge of the waveform represents the 'input' and the trailing edge the 'output'...
Fuses tend to be measured by length and diameter as well as the amperage rating.
The 125V is a misnomer - the 3A detail is important. Measure its length (20mm? 32mm?) and you'll find there are many available
Given that different plastics melt at different temperatures there is no reason why a standard glue gun couldn't be adapted using some form of temperature control to allow any type of plastic to be used. Fit a thermistor and use a soldering iron digital controller to set the temperature for...
Use a waterproof in-line plug and socket
https://www.ebay.co.uk/p/Ip66-Waterproof-Outdoor-Garden-Pond-Electrical-Cable-Joiner-Connector/1554306761?iid=401387446723
or mount an IP65 rated box and join internally through suitable glands.
But a lot depends on what the cable is being used for...
What are the actual power output voltages? I think I can see a 12V line - are there any others?
I'm thinking you could remove Q1 and the transformer, apply the 'missing voltages from a different PSU straight to the output terminal block, leaving all the other connectors in place (for the relay...
'Join' under what circumstances?
Indoors, outdoors, fixed, flexible ?
Inline crimps, chock block, resin-set, terminal box? twist,solder, heat-shrink?
Soldering is acceptable under some circumstances and won't melt if the conditions are met.
Check the fuse (F1) likely blown.
Check Q1 - likely shorted.
The IC is probably an SMPS controller device - what type number is Q1?
Show the actual top of the blown IC.
Sounds like you have an intermittent short circuit or possibly some moisture in the wiring.
A resistor won't help. What make/model is the system? What kind of wire are you using between push-button and chime? What length is this wire?
Use the device that was oroginally intended to drive the motor - either salvage it from the HDD board or purchase a new one of the same type.
Such motors are generally '3-phase' (for driving requirement) and there are a number of methods to get them spinning. Have you Googled for them?
Check for broken or stretched belts on the internal mechanism.
TBH an old VCR is a combination of complex electronics with even more complex mechanics - not something that anyone of little experience would have luck in repairing. This is likely to be a professionals task and a rare (ish)...
Any more information on the humidifier? Make, model etc? A picture of the pcb and area around where the IC was originally located may help us identify it. That code shown is meaningless (to me)
Have a look in your local Lidl (or Aldi) store as they have them all the time. CHEAPER than the Chinese source and you'll also get a 3 year warranty, guaranteed UK operation and abundant spare glue sticks off-the-shelf.
https://www.hotukdeals.com/deals/parkside-hot-glue-gun-799-lidl-2681784
There are an abundance of cheap digital timers that could control your power pack(s) that drive the LEDs. Use separate timers for each colour and program the cycle however you require.
Mount a few of these in a box...
I wouldn't take a continuity reading from that switch as definitive proof it's working (properly). I recognise the the switch 'type' and they are quite notorious for intermittency and failure under load.
Use a crocodile clip (insulated) to physically short the switch contacts and try powering...
Rework station???
On a DIY basis you could use the element from a clothes iron 'pinched' between a thinner plate and the main pad. Drill a small hole to take the thermocouple (heat sensor) then it would be a case of calibrating it.
There are a good many temperature controllers available on...