What metals are generally used in electrical wires

This is a very good question. In general, wiring in your home and in devices are pure (or at least 99.9% pure, due to difficulties of purification) copper. So, whether it's phone chargers, or microphones, it's all still copper. You will however feel a difference in the physical properties of the cables due to the type of insulation, and how stranded the copper is.

But when are other metals used in conducting electricity?

Gold
Gold is a worse conductor than copper and silver (and more expensive), but resists oxidation much better. As a result gold is used to plate connectors, whose connection may degrade if the surface is oxidized.

Gold wire is also used in chips to bond the interconnects between the silicon and the chip package. Gold is used as it resists oxidation when bonding. Copper can also be used, but would need to be done in an inert atmosphere like nitrogen.

Silver
As you mentioned, silver has a higher conductivity than copper, but isn't used widely due to its cost. But it does have a few niche uses where extremely low resistance is desired, such as in sensitive scientific instruments; cryogenics (where it's desirable to have minimal heat generated in wires); and also in electrical contacts in switches, where the softness of silver and relatively good-conducting silver-oxide makes it a good choice for metal-to-metal connections

Aluminium/Aluminum
Aluminium conducts less well compared with copper - for a given size of cable copper will conduct better; but because aluminium actually has a better weight-to-conductivity ratio, aluminium wire with the same conductivity as copper wire would be physically thicker, but would still work out to be lighter, and probably cheaper too.

Due to this, many overhead power lines are made of aluminium - the lower weight is a benefit, and physical size isn't an issue.

Some aircraft wiring is made of aluminium to save weight; as are some motor windings where weight is important.

Aluminium is also sometimes found in old domestic wiring from the 60s or 70s during a copper shortage that caused copper prices to rise.

Tungsten
Tungsten is used when you actually want the wire to have resistance, and also have it not melt even when white-hot, as is the case in incandescent lamps.

Alloys
There are many different alloys used in electrical conductors. Here are some examples:
- Nickel-chrome (nichrome) wire, like tungsten, can survive high temperatures, and the higher resistance is desirable. Being cheaper than tungsten, is used in heater wires, where the wire doesn't need to get white-hot.
- Solder, which is an alloy of tin and lead, or other mixes of metals in the case of lead-free solder, is used for bonding electrical components to copper pads on PCBs. The low melting temperature of tin-lead makes it suitable for this task.
- Cryogenic wire is often phosphor bronze (copper, tin, phosphorus), where the resistance of this alloy doesn't change much at very low temperatures.

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