Will closing the laptop screen without putting it to sleep damage the computer?

Closing the lid is a normal action on Windows laptops. What matters is the setting behind it. Open Control Panel > Power Options > Choose what closing the lid does, and set separate actions for On battery and Plugged in. For everyday carrying, Sleep or Hibernate is usually the better choice. If you use an external monitor and keyboard at a desk, Do nothing while plugged in can be convenient, but make sure the laptop has ventilation. Before putting it in a bag, confirm it is actually asleep or shut down so it does not keep running and heat up.