I wanted to know if it's possible for a website to record the screen or take screenshots of the screen or of the webpage itself (for example to monitor what the user is looking at on the website)
thanks
Yes, websites can understand which key on keyboard you type, so if you hit on printscreen button on windows, active open website can understand you take a screenshot. No, not really. Some apps like Snapchat will tell the other user about a screen shot.