I have a lot of experience with the Bitcoin industry, but little experience with the Stock Market. In the bitcoin industry, when you want to buy/sell, you have to put out a market order on whatever exchange you are currently using, but usually the market order isn't always at the current "market price".
For instance, when you sell Bitcoin, you'll usually sell into someone's current buy order, for a $1-2 less than current market price. Similarly, when you want to buy, you set a "buy price", and absorb any sell orders at that price point.
Are Stock markets similar to this? Is there a standards bureau behind the market that all stocks are bought/sold through to make sure that all stocks are bought/sold at the current market price? Are you always able to sell a stock even if there is no buyer? Are you allowed to sell a stock for half of it's market price if you really wanted to?