Update:
So i reset the phone, using the
Settings > Reset > Restore settings menu,
and after re-inputting the settings, the Mail app started to work again.
However, it got stuck mid-way through downloading the emails from the configured account, and asked "Mail not responding? Close/ Wait."
After I closed it, the earlier issues of not being able to open the app, or certain menu items in settings, have returned.

Any idea what could be wrong?