The fuller sentence would be:
First graders have been seen to be willing
With 'watched' the collocation would be something like:
First graders have been watched as they worked on...
This changes the meaning, from how the children 'were willing to work...'
2. 'illiterate': unable to read or write
So - practically illiterate means almost, nearly unable to read and write.
They are most probably not as bad as that, but their level of vocabulary and so understanding of the words in newspapers; and being able to comprehend the meaning of what they are reading is so poor, that in terms of when they are asked to perform the tasks of "reading a newspaper, filling out a job application or balancing a checkbook", they function very poorly - hence, functionally illiterate.
For example, if an application form had a blank for "Gender' they may be blank as to what they need to write there!