How to remove ‘Always on Layout’ and ‘Required’ field from the page layout (blue circle and
red asteroid next to this field)?

Answer: To remove field which is ‘Always on Layout’ and ‘Required’ on the page layout, first make it not compulsorily value required by properties -> uncheck ‘Required’ on page layout itself (click on the wrench symbol next to the field on the page layout), then go to each profile and in ‘Field level security section’ uncheck ‘Visible’ checkbox.