1) Cream is basically milk with a high fat content. It tastes good and is more expensive. 2) Creamer is a fake substitution that sometimes has some milk in it, but sometimes has no milk in it. Most offices want to save money, so they buy creamer for their employee's coffee, instead of actual cream. Although many people prefer creamer for various reasons. (For example, if they are allergic to dairy products)

Correct. Creamer is not from a cow

This is partially correct. Cream is a fatty component of milk that is extracted with a centrifuge or filtered. It is high in fat. Creamer is originally a vessel that lets you serve cream at the table. The word is also used by companies that make a non-dairy product to put in coffee instead of milk or cream. They are often low fat, flavoured and sweat.

Correct. Types of creams for baking such as light cream or heavy cream that are liquid. Creamer is like a powder to add in coffee.

I’m not a native English speaker, but I would say that « creamer » is an industrial product used as a cheap milk or cream replacement for adding in tea or coffee. Some creamers are liquid, some look like powdered milk.