Hope you are doing well and sorry for the trouble. As described the fill and sign tool is empty and you do not have the option to sign the PDFs
Would you mind sharing the version of the Acrobat Reader DC you are using? To check the version go to Help > About Acrobat and make sure you have the recent version 22.1.20117 (Win) , 22.1.20112 (Mac) installed. Go to Help > Check for updates and reboot the computer once.
Also, try to repair the installation from the help menu (Win Only) Help > repair installation and check. You may also try to create a new test user profile with full admin rights in Win or enable the root account in MAC and try using the application there and check.