The "all else being equal" part is critical here. In reality, all else is never equal. Deflation is the reduction of money supply relative to the available pool of goods and services. That is, you can have a fixed money supply and still have deflation if the pool of available goods and services is expanding (which is usually the case, as human civilization progresses). That's why they say that Bitcoin is a deflationary currency. Or you can have an expanding money supply and still have deflation if the pool of available goods and services is expanding even faster. That's why they say that gold is a deflationary currency.
No, deflation isn't "caused" by that. Deflation is the reduction of money supply relative to the available pool of goods and services.
It is falling prices that are caused by falling money supply or falling demand for products (among other things). Most people know that prices depend on the balance between supply and demand. Few people realize that they actually depend on the balance of four things:
1) The supply of products.
2) The demand for products.
3) The supply of money.
4) The demand to hold money.
The last one is especially difficult to quantify. Basically, money is a good like any other; the good with the highest liquidity. The laws of supply and demand apply to it too. In fact, products are always paid with products; money is just the medium of exchange.
True in general but the reality is a bit more complex than that. It depends on what time we are talking about and how much the currency appreciates during this time. If the numbers involved are relatively small (i.e., deflation is mild), most businesses will still thrive.
Exactly. And if deflation becomes stronger, this can increase the demand to hold money, putting additional downward pressure on prices - the so-called deflationary spiral. This is what happened during the Great Depression and this is what has the mainstream economists scared to death. A simple, mild deflation isn't really a problem and can be actually beneficial for the economy, since it stimulates savings and savings are equivalent to investments and capital accumulation.