Say I invent something and choose not to patent it but start producing and selling it, then if somebody else goes and patents my exact design what happens to my rights to sell/produce that product?
If you are producing and selling it, that is an absolute bar to patentability by anyone else (this is known as prior art). So if you are using it very publicly before they file, they can't get the patent.
The U.S. is a first to file system of patent. If someone patents before you, they own it. It happens all the time: a bigger company steals an idea and patents it before some small inventor can. It costs a lot and takes a lot of money.