The different Wi-Fi icon at the top left side - Not sure what that exactly it is. Probably the signal strength of your cellular service however it appears on the right side on the home screen.
Crescent Moon Top Right Side - This is the Do Not Disturb symbol however it should not be visible on the home screen.
Partial White Bar under the Battery on the right side - This is the bar that suggests the user to touch and pull down on it to reveal the Control center. But this is only visible on the Lock Screen.
Is it possible that you may be calling the CONTROL CENTER as the Home Screen? Because if you are looking at the CONTROL CENTER then I can explain all of the above.
The different Wi-Fi icon at the top left side - Cellular Signal Strength
Crescent Moon Top Right Side - Do Not Disturb is set to ON. To turn it OFF, open Settings ➔ Do Not Disturb ➔ Set this to OFF.
Partial White Bar under the Battery on the right side - This is the bar that suggests the user to touch and pull down on it to reveal the Control Center however you will mostly see this on the Lock Screen.
Axel F.