Ok- lets say a wall socket is providing 300V, at 200A. If I plug a device into that wall outlet, and this device has a 13A fuse, will the fuse blow, since the amperage being delivered is over the threshold of the fuse? And, from what I have read, why does a fuse even exist in the first place- if a device was to short out, or fail, then why should it use anymore current than it was already using? I just cannot wrap my head around this concept, and have tried googling this, and tried using all these different analogies, but electricity in general just baffles me.
In short, a fuse is nothing more than a controlled failure.
If too high current flows into a circuit, a too large power is generated, $$P=I^2R$$Components and wires all have a limit of how much energy they can absorb before melting or burning. If you let it go wild, you will not know which component or wire that will fail first. Maybe an expensive one, a hard-to-replace one, or maybe one that risks causing a fire.
So, to avoid any such random failure that could be catastrophic because we have no clue of where or how severe it would be, then we instead add one component with a lower durability than all other components, parts and wires. And then we make that weakest component of a material that melts rather than burns with flames and we incapsulate it to keep it controlled when it fails. Maybe we even place it on an accessible place so we can easily replace it when failure does happen.
That weakest component is the fuse. It is simply a component chosen to be sacrificed, so that all others will survive.
Amps are a measure of current or electrical flow. The wall socket just sitting there will have connectors that are often at a different potential. Let's go with your scenario that they differ by 300V.
But since they're not connected, there is no current flow. The current before plugging anything in is exactly 0 amps. The 200A you mention does not mean that the socket is always delivering any particular current. It could be a design limit of a particular socket (a maximum rating). But 200A would be incredibly high for a home circuit.
When you connect an appliance to the socket, it (normally) completes a circuit and allows electricity to flow. But the design of the device determines how much flows. You can plug in a night light and it will draw only a few milliamps. You can plug in a hair dryer and cause more than 10 amps to flow. So just plugging in a device or using it properly doesn't cause the fuse to blow.
Overcurrent causes heating in wires, connectors, and other electrical components and is a fire risk. A short in a device allows more current to flow, and will heat components in the circuit (that includes wiring inside the walls). The correct fuse is designed to heat and fail quickly when limits are exceeded. When the fuse opens, it should stop all electrical flow, preventing fire or additional damage from continued heating.
The important expressions here are $I=V/R$, which relates the current ($I$) to the voltage ($V$) across a resistance ($R$), and $P=IV$ which relates the power ($P$) dissipated in the resistor to the current flowing through it and the voltage across it.
The wall outlet provides a fixed voltage. When a device is operating normally, it provides a fixed resistance, which in turn results in a reasonable power dissipated in the device. But if there is a short, then R goes really low, causing the current $I$ to shoot up (since $V$ is held constant). Thus, $P$ will also shoot up in the regions where there is still some residual resistance (e.g. the wires), causing a lot of extra heat to be generated. Since this extra heat can cause fires, people use fuses, which are little resistors designed to burn up/melt relatively easily. The fuse melts before anything else does, breaking the circuit and shutting down the current.
If your wall socket is rated to 300 V and 200 A, that means it can withstand 60 kW of power before it burns up. That’s much higher than will normally be flowing through it. Your fuse is rated to a much lower power because you want the fuse to be the limiting factor in your circuit. If anything melts/burns, you want it to be the fuse.
No, the fuse on the device won't blow!
The reason the appliances have fuse is to protect their circuitry, or if they are electronic appliances like TV or computer, protect their sensitive electronic systems. Sometimes because of a surge or intermittent fluctuation in the plug power coming from the electric company the appliance fuse would trip, or burn, preventing damage. But if you connect an appliance with lower amps rating than the circuit it plugs to it's ok.
I would use only as much amps as it can, not any more!