Under the U.S. stock market trading system, most of the transactions are conducted through specialized dealers and market makers. They are only required to notify the public within 90 seconds after each deal is made. In this case, the information we see is delayed on all real-time market systems.
In the U.S. stock market, the unit for buying/selling shares is one. However, in order to reduce the transaction cost and lower the risk for stock holding, dealers and stockholders will trade in unit of 100. In this understanding the unspecified one 「lot」is 100 shares. If the investors place orders not in multiples of 100, they may need to wait a while.
The pool for stock shorting may out of stock when the short orders are placed, however, the order will not be rejected immediately. If the pool has incoming stocks with proper price, the order will be executed later, if the pool does not have any incoming stocks by the end of the day or the incoming stocks price is out of range, the order will be withdrawn.