Is it permissible to remove the ovaries after repeated childbirth and the last child being afflicted with Down syndrome, and due to the harms resulting from the use of birth control pills, such as tumors and ulcers in the cervix?

Completely stopping procreation by removing the ovaries is impermissible except out of necessity and severe need. The determination of such a necessity is to be referred to trustworthy doctors. If there is no justification for completely stopping procreation, but there is a benefit in delaying it temporarily, then there is no harm in using suitable birth control methods.