Bosda, I don’t believe there is any way to save data with the free reader. You will either have to finish and print the application all at once, or print the application and fill it in by hand.
A way around that is to transform the PDF document into a TIFF document and then you can use IMAGING which comes free with Windows. Imaging allows annotations etc. I use it quite often for that type of thing. I’ll scan documents I have to fill out regularly (like a visa application) and just change the date and whatever else I need to change. I even print my photo on the original document. One time some guy at the window was trying to get his nail under the “photo”. It took him a while to realise it was printed on the same sheet.