Hope you are doing well and sorry for the trouble. As described you are not able to add or change any of the field when you open in Adobe Acrobat Reader DC
Web browser use their own PDF mechanism to display and render PDF files and they are not Adobe dependant.
Also Acrobat Reader DC is a freeware application, it is used to view, read, annotate, fill and sign the PDF files. Please download the PDF file to your computer and save it locally and then try to fill the form and check. For more information please check the help page https://helpx.adobe.com/reader/faq.html