Some of what you are describing sounds similar to an investment club in which members have varying ownerships in a common pool of securities. They are not considered exchanges.
As you might guess, Starting up a new exchange doesn’t happen all that often.
You would need to be compliant with the Securities and exchange act of 1940. You should be able to find information on that at the Sec’s web site, or e-mail me your address and I’ll send you a book on either investment clubs or the SEC.
You may be misconstruing what constitutes a stock. The actual certificate has little meaning these days.
Today, many if not most securities are issued in electronic (book entry form) only.
When we receive physical securities at my firm, we eventually destroy them.
What is important is how the name is held at the registrar for the security. THAT is who owns it for all intents and purposes.
To make your exchange work, you wouldn’t necessarily hold certificates, so much as track transactions and provide “good execution” (a fair market.) You would eventually need to hook up with the DTC, the delivery transfer corporation which is a government corporation that tracks transactions on a daily basis. I have no idea how you go about doing that though. The NYSE is simply a place. The NASDAQ is simply a conglomeration of market makers. I’m not sure what functions of an exchange you are looking to emulate, but they do not serve as a repository for certificates, even in book entry form.
Think of owning a flea market. Every day people bring in tables and merchandise, sell it, and every day all those tables and merchandise is gone. All you own is the hall.
So:
A: Yes. People can buy and sell stocks anywhere they want and frequently do. Nonexchange traded stocks change hands only in this fashion. An exchange though gives you a more liquid and continuous market. Will there be people in your living room 24/7?
B: Can’t do that. You are either a brokerage firm, investment club, or mutual fund (investment company) and must conduct yourself as such. You are not an exchange.
C: Not sure how to answer as per previous problems. The exchanges are self-regulating. You will most surely be held accountable to the SEC and must report your transactions to the DTC though. Again you might not be an exchange, but an investment co., club, or member firm.
I hope that helps.