Did you save the PDF as an Extended Rights PDF? You will need to open
the PDF in Acrobat, go to Save As Other and Select "Reader Extended
PDF". This will allow you to do things like save data in Reader.
Yes, you can do this quite easily. On the object palette, click on the
field sub-tab. There is a size field; if you want the checkbox larger,
increase from default size of 10pt to 14pt or whatever size you want.