You can't fill the form on the iPad. Use Acrobat Reader on Windows or Mac.
Hope you are doing well. Sorry for your experience with Acrobat Reader Mobile.
As Bernd mentioned, you can best fill this form using the desktop version of Acrobat Reader or Acrobat Pro DC.
The file you shared is created using InDesign with a few compatibility issues when trying to edit using Acrobat Reader for Mobile.
Also, the file is restricted for most of the functions except printing, commenting, and filling forms, due to which Reader Mobile cannot bypass the security.
Considering you do not possess a computer, I suggest installing Adobe Fill & Sign application from the App Store. This will help you fill out the form.
You can install it from here: Adobe Fill & Sign－Form Filler
Hope this helps.