You can do as much as you want, or as little as one single square during the amnesty period. If you want to earn points you have to do at least one line bingo in the time allotted, and then you can do 'extras', like doing every single square (which is called a blackout and I'm sure is worth BIG points) or just continue doing line bingos.

Also once you've completed a single bingo you can ask for a second card if you want!