Why has a red flower appeared in the middle of my opening screensaver?

That is simply the icon assigned to your user profile on the computer. Open System Preferences - User & Groups - Your Profile: Rest your mouse over the Red Flower Icon by your name and click "Edit". Here you can change it to an Icon better suited.

Now that you know what it is, get rid of whatever you used to perform a "virus scan". Those things are categorically worthless at best, and are often harmful.

Follow its uninstallation instructions, assuming you can find them, and that they actually work. Most of them work with less than complete effectiveness.

If you exceed the allowed max inactivity time, for security reasons you are required to reenter your password.

That's just the user image you've selected.

System Preferences > Users & Groups

change it to anything that you want

That's a default icon. You're going to have one regardless, you just need to understand the process.

if you like, you can use the same process and ask it to take a "selfie" picture of you as your identifying Icon.

Perfect. Thank you for the feedback.