How is it possible for there to be trading "premarket" and "after hours"? I thought the exchange is closed and thus trading during "premarket" and "after hours" is impossible. Are such price changes "premarket" and "after hours" caused by changes in stock futures?
The value of things change continuously. Take for example oil. It can close on Friday at $50/bbl, and then on Saturday the Saudis could have one of their large processing facilities destroyed. This would have a meaningful impact on the global supply and demand balance, such that you, and everyone else, can reasonably expect that the supply has been reduced, and so the price can be expected to be higher.
The transparency in the market is for sure reduced out of hours, you cannot just use the exchange for price discovery, even on exchanges where the bid/offer can be changed outside of hours without trading (which gives you some idea of the level), because there is no trading the setting of the prices means considerably less. But this is another point.
What you will see is that upon opening, the price will quickly move to be in line with those previously mentioned expected (different from the closing) levels. In some cases, where the exchange is closed but you're able to clear out of hours, the price may be updated out of trading hours as trades are cleared.
As for "how is it possible", this is just infrastructure and people not arbitrarily saying "sorry, closed, can't help."