You can hide the welcome banner with the Enable welcome banner site setting.
For the header, take a look at the Brand Header component.
I am not sure which change you want for the search and menu icon. When you are logged out, you will see the sign-up and log-in buttons. When you are logged in, like in your first screenshot, you see your avatar, which opens the notification menu. Can you explain what you want to adjust? The background color is based on the color palette.