my power-adapter burnt as i plugged it to wall socket

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is the component behind the ceramic capacitor a fuse? if it is, why it didn't handle the shock at first and save the other components?

The fuse is a overcurrent protection device, but your power supply failed due to a voltage spike. When the mosfet shorts out, then the fuse will open to insulate the circuit and prevent a dangerous overheating. The build quality does not look good at all. Muntzing has been applied mercilessy on this device, no wonder it failed. The white dash on the back silkscreen does mark the spot to bridge with solder to bypass the thermistor and fuse, and save some extra cents if needed.
You can recover the two big low voltage diodes at the output and the green led, because is quite easy to check it they still work and they may be useful for several projects. Everything else is not worth the recovering/testing effort.
 
It is relatively low the chance that a kind of such failure blown the fuse. Those low power resistors are by far much more delicate and the power involved is larger in them as the resistance is higher than of the fuse and the termal inertia shorter. I saw at job thousands of those psu completely destroyed but the fuse.

I desagree that a voltage spike has blown the psu. The first time component damaged usualy is the source/emiter metal foil resistor that doesn't support initial current spike in it.
In my first smps build, I had this problem. When repaced with a wire wound resistor, the problem dissapear. Once the current in this resistor destroys the former, as there is an inductance in the drain/collector; can't continue flowing and a high spike of voltage appears that destroyes the gate/base and then the current now flows through the driver avalanching what it founds through its path. Remember that in an inductive circuit current can't change instantaneously as voltage does. In doing those change, time must flow and voltage reacts in the way of try to mantain current in its initial state.
 
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It would prevent a catastrophic current flow that could start a fire.

The current needed to blow those components apart is actually pretty small, way below what a mains fuse would pass.

NTC generally are for inrush suppression, a PTC will provide moderately fast fault protection by limiting current.

I assume this is an NTC.

I recommend buying a decent DVM and a new power supply.

I know you are not planning on repairing this, but even if you were an incorrectly repaired or badly designed/manufactured SMPS is a safety hazard.

Please buy one with a safety certification, usually CE / VDE certified supplies will be safe if the marking is not faked.
 
I had a look at the board pictures, and the supply looks like a poor implementation of an RCC design (ringing choke converter). It looks like there is no snubber to speak of on the drain/collector, which might result in a tendency to explode violently. The worst thing you can do to an SMPS (except for shorting the output) is turn it on, so if there is a significant weakness in the design, that would be the time for it to manifest itself. Poor design, cheap parts - trouble... If the design is a ringing choke and using a mosfet, a single pull-down transistor would cause non-optimal turn-off for the mosfet, a recipe for disaster. I use a pnp/npn "bisexual SCR" in my RCC designs using power mosfets, so that the gate gets pulled down quickly and cleanly.
 
Here the RETAIL price for a cell phone charger starts at about 80 cents, which means the maker is lucky to get 50 cents.
12V/1A supplies, $1.20 upwards, retail, with flying leads.
12V/2A in metal case, decent parts are $3.50 and up.
The cheapest ones use a single MJE13001 transistor and some sort of Zener, there is no opto coupler, and a 2 Watt or so series resistor, as fuse, current limiter and so on.
Welcome to the El Cheapo world.

I can see you reeling in shock...