Can the anti-cheat read my open webpages or record my input when the game is open?
We're not interested in your browsing habits.
It's important to know though that almost every program on your computer can record your input or read your open webpages. This is because it doesn't take any special permissions to do so (not even admin access in many cases).
If this is something that you're worried about I recommend being extra careful about the software you install.