If you're having trouble downloading PDFs directly to your iPad, use a computer or laptop to download the fillable PDFs. Next, save the PDFs to iCloud or any other cloud service you normally access on your iPad. You should then be able to open the PDFs from iCloud or another cloud service on your iPad.
If that doesn't work or it's just too complicated, here's a clunky email workaround: Save the PDFs to your computer. Then, email them to yourself. Open the email on your iPad and open the PDF attachment(s). Choose "Open in..." to open the PDF in the app of your choice.