I see orders being placed in the middle of the night on my trading screen for nyse stocks. who has the ability

Answer 1

I do.

Just because a stock is listed on the NYSE doesn't mean it has to be traded there. It can be traded anywhere that a buyer and a seller can agree on a price.

Some are dual-listed on other exchanges, but what you are probably seeing is Electronic Communications Networks where people and institutions can post prices at which they want to trade and see others prices. The ECN computer then matches them up. The NYSE actually owns an ECN.