What’s the difference between words “number”, “count”, “amount” and “quantity”?

Number(v) = Give something a number.

There are 4 apples, number them.
a large/small number of (n) = To measure ANYTHING when we don’t know exactly how many

There are a large number of people at the beach today.
Count (v) = How many are there.

Count the apples.
There are 4 apples.
Count (n) = How many of something are there.

What is the apple count?
There are 4 apples.
Amount to (v) = To measure something, not alive, which CAN NOT be counted.

The meeting between China and the USA amounted to nothing.
Amount (n) = To measure something, not alive, which CAN NOT be counted.

There is no amount of money that will make me do that.
quantity (n) = To measure something, not alive, that CAN be counted.

There is a large quantity of stores in the shopping mall.
In common conversation you can always use “a lot of” to describe any large number, amount or quantity and “not many/much” to describe any small number, amount or quantity.