1st What are the 3 most common types of faults in toasters?

Attributed iFixit repair guide for Toaster.

iFixit Library Toaster Easy 2 hours Guide 220359

Licensed iFixit integration

This attributed iFixit guide is displayed through Fixonic's recorded commercial API permission. iFixit remains the independent source and author of the procedure.

Step 1

Checks.

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1st Fault: the machine does not latch, but it does heat up. Power input contacts "contacts" are very charred, burnt, or too far apart; when the lever is lowered, the circuit does not close.
You must check the cleanliness of the power input contacts and the separation between both, which should be minimal. If they are too far apart, when you lower the lever they will not close the circuit; this can be the problem, or there could be bread crumbs and grime on the electromagnet that latches the mechanism.
Video example of how to rule out a latching or broken Nichrome wire problem.
iFixit document with a real example of this fault and its solution.
The solution is cleaning the 4 contacts with a nail file.

Step 2

Repair step

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2nd Fault, Dirt and breadcrumbs in the electromagnet and the metal plate that closes it from above, this problem is usually related to the one in the 1st step and when the contacts are cleaned, this is also checked and cleaned.
Bread residue, crumbs, and dust on the metal plate that closes the electromagnet and locks the lever when it is lowered; if there is a lot of accumulated residue, the electromagnet tends to come loose and the metal plate does not remain locked.
IFIXIT document example of this fault and solution:

Step 3

Repair step

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3rd Typical failure in toasters, breakage of the Nichrome wire, so when the operating lever is pushed down, the toaster does not heat up at all.
Before we get into checking the Nichrome wire, check that there is continuity between the power input plug and the contact points (contacts) on the electronic board, as the power input cable may be broken internally at one of its bends.
Once it is ruled out that the cable is okay, we move on to checking the Nichrome wire; we will have to locate the breaking point and fix this failure once the break point is located, by repairing it with a bolt + nut + 2 washers.
Example video of how we would carry out this basic check:
Example video of how we would carry out a basic status measurement of the Nichrome wire.
iFixit document example of a real step-by-step repair.

Step 4

Repair Example.

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Process for checking and repairing a toaster with a broken nichrome wire.
6 Videos showing the step-by-step process.
iFixit documents: Mandine MT 8616-16
Useful DIY tools for repairing a toaster: Toaster

Step 5

Repair step

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Other failures: If you have reached this point and have not solved the problem, and none of the 3 above are the issue, things get a bit more complicated, we would move on to check with a multimeter on the ohms scale:***
Burned electronic board resistor acting as a fuse, open: You can more or less see the value, it is usually about 47 ohms approx.
Interlocking electromagnet with a burned, cut coil: This would be irreparable given the impossibility of locating a suitable spare part. iFixit example document
Having arrived here, we are now at the final point; if you have not located the problem and have ruled out everything above, the next steps make it quite difficult to continue the repair.
Other electronic board failures: It is rare to reach this point, having checked and ruled out everything above, but it can happen. NOTE: also check the solder joints of the connectors between the 2 electronic boards if the machine has 2 boards.
It is rare to reach this point, but if you have arrived without managing to locate the problem, I do not advise you to spend more than 1 hour checking the board and testing components, as honestly, it is a waste of time with such a low-cost machine.
Without an electronic schematic, it is extremely complex, and your time is too valuable to waste on such a low-cost machine.
End of the Guide.