"How much would it cost?" There a lot of variables here. First you need a mold. This can cost anywhere from $2,000-$3,000 up to $50,000+ depending on the complexity needed to make your part. You could probably have "soft tooling" made (aluminum mold inserts) for design verification for around $1,200 - $1,800 for a simple two platen mold with a single parting line. You will get a limited number of parts from this setup before the mold brakes down. Next you need someone to mold it for you (assuming you don't have a mold press in your back yard). They will probably ask how many parts you need and probably quote you a price per part to have them molded. You will also want them involved in your mold design. Many times they have pre-built standard mold frames that allow you to add simple, inexpensive tooling. Each mold frame differs slightly, and each mold press differs slightly so you don't want to design a mold on your own only to be told it will need to be re-designed to fit in the mold machine, or mold frame.
"What type of manufacturers do you contact?" An injection molding house.
"Where do the manufacturers reside?" All over the place. Type "injection molding house (your town name) (your state)" into google.
"How much upfront money do I need?" Probably $10,000±
"What type of file format do they want?" They will want technical drawings of your part. For some complex parts they like to have a solid model file, an stl file usually works.
"How do you proof their prototypes?" You recieve the first few and check them, either by eye, or measurement tools. If you need to you can have a machine shop QC the parts based on your technical drawings.
"Would you do it again?" I have not done this for myself, but the company I work for does it in conjuncting with the mold house that resides accross the street from us. I design the molds for them. The people that have had it done are happy with the results and move on to make thousands of parts usually. Believe it or not (and this bit hurts), having parts made is the cheap part! Sales, marketing, distibution, and quality control are going to kill you unless you have stumbled upon a widget that everyone must have! I have been in your shoes and I do not mean to shoot down anyones dreams, but unless you have have something you can make millions of and live with a profit of about .1 cents per part someone else is going to mass produce your idea. The Someone I mentioned is going to be a large company with far more capitol than you, and an in house molding facility that will churn out billions of your part. Protecting yourself with a patent is rediculisly expensive, time consuming, and frustrating so this avenue is fairly unatainable for the average person, but if you can pull this off selling the patent to a large company with an agreement to collect royalties is an easier move.
If you want to let someone look at your part feel free to contact me personally (not the company I work for). I can tell that you are concerned about somone walking away with your design, but I can assure you I do not have the capitol, or intrest in doing so. Good luck! I hope I have given you some insight.