Please help understand how a household electrical component works in context of step down voltage and ampere?
I'm going to offer a slightly different tack than the other responses, as you already have enough there to work from. And perhaps a different approach might also help a little. (Or make things worse.)

You may not understand the difference between having the capacity to do something doesn't mean you are actually doing that something. You might have the capacity to lift 100lbs, but that doesn't mean you are always in the process of lifting 100lbs. You might be lifting only 1lb, at the moment.

You bring up a transformer almost immediately. So, let's take that. Buying and using a transformer that has the capacity to handle 100W of power, with its primary side designed to accept 117VAC @ 60Hz and its secondary side designed to deliver 12.6VAC @ 60Hz, doesn't mean that it necessary MUST consume 100W of power at the primary and then magically and forcefully deliver 100W of power at the secondary. It merely means that it may be able to deliver up to 100W, if the secondary load requires it. Not that it must do so if the secondary load isn't present or doesn't require it.

Power can be considered, as you noted, the combination of two things: I and V, or amps and volts, multiplied together. This is like the area formed from the two sides of a rectangle, though.

Most practical systems are designed around setting a voltage (one side of that rectangle) and then allowing the other side (current) to be flexible and to adjust itself. The current is compliant to the area requirement, while the voltage is not compliant. So a device is hooked up to a voltage source, which is not compliant, and draws what current it requires, which is only limited by the ability (compliance) of that voltage source. The voltage source will have a current compliance figure, which is a maximum that a device can reasonably require.

A device hooked up to the voltage source may require a certain power. This means a certain area, in effect. The voltage source is fixed and this sets one side of that rectangular area. And to achieve the needed area in the rectangle, as required by the device, the current adjusts itself (assuming that the voltage source is sufficiently compliant to do so) so that the required area (power) is achieved.

Some power supplies may have their power set in stone, too, as well as their voltage. In such cases, they dissipate as heat what isn't used by the device or load, while performing their other job which is to keep the voltage well regulated. Some power supplies adjust their own loading on their own source automatically, so that they don't dissipate so much as they might otherwise have to. (They may also temporarily store some energy inside themselves, holding it for later use a short moment later.)

There are cases where a power supply doesn't regulate the voltage, but instead regulates the current. Certain kinds of welding, such as SMAW, prefer to use constant currents. So the current is regulated (fixed) and the voltage is the compliant value (which must be within the power supply's compliance rating for voltage.) So, while constant current supplies are not as commonly found, they do also exist.

But power is like area in this sense, with voltage as one side and current as the other side of the rectangle.

Reactive components complicate the understanding a little, because they can temporarily store energy in one of two ways: a magnetic field or an electric field. An inductor stores energy in a magnetic field and a capacitor stores it in an electric field. These temporary sources of energy can be added into, or subtracted from, at different times. These can be used to advantage in a circuit. It's even possible to transfer energy between a capacitor (energy stored, showing as a voltage across its terminals) and an inductor (energy stored, showing as a current through its terminals.) And if they were perfectly efficient in transferring energy back and forth, they could keep doing that transfer between them, back and forth, for a very, very long time.

EDIT: I suppose it may help for you to think of voltage as equivalent to the air pressure presented by an air compressor. If it is at 150psi, that's a certain pressure similar to volts. You can now hook up different attachments, in order to use that pressure to do work. Some of these, like an orbital sander, will permit a lot of flow (cubic feet per minute, or CFM) in order to operate the sander correctly. The design of the orbital sander determines the needed CFM compliance of the air compressor system. And in fact, a lot of air compressors won't properly operate an orbital sander continuously because they can't keep up with the CFM required. They don't have the capacity. Think of the CFM as current, here. Then air pressure is like voltage. Different devices will be designed to use different CFM in order to do their work. Ones requiring less CFM will have higher resistance to the pressure they are exposed to. Ones requiring more CFM will have lower resistance to the presented pressure. These resistances are designed into the tool. And they are usually designed to operate with a specific pressure and CFM rating. And you need to purchase an air compressor that can support the CFM rating at the indicated pressure.

I suppose you could imagine also that the operating power, in this scenario, is the air pressure times the CFM being used while operating the tool. The compliance of the air compressor is the average air pressure it can sustain times the sustainable CFM it can simultaneously deliver, if asked. More sustainable CFM (for a given sustained psi, such as 90psi) means a more powerful unit. (And a more expensive one.)

Many air compressor attachments can still work at widely varying pressures, if poorly at times. Electronic circuits usually depend a little more on a specific voltage level, by comparison. But the basic idea generally holds and some electronic devices (such as the charger for my Nikon Nivo 5C Pro, which accepts any AC voltage from 100VAC to 240VAC) can indeed still operate well over a wide power supply voltage range. So perhaps the analogy still holds, even here.

Finally, consider using just a small nozzle to blow sawdust off of your table saw. That nozzle works great at 90psi, just as the orbital sander does. But it uses a lot less CFM. It has more resistance to the pressure and let's far less air escape per unit time. The air compressor has nothing to say about that, too. It is up to the tool to decide.