There are a few books on Google Play that are free. Can I obtain said books without providing a credit card number?
Looks like it depends on the book. From Google Play support:
Downloading free music, TV shows, and certain free books and magazines is still considered a transaction, even when the price of the item is $0.00. If you don't have a credit card associated to your Google Wallet account or if you don't haven't set up a Google Wallet account, you'll be prompted to add a new payment method upon when downloading certain content from Google Play.
Google has released an app called Google Opinion Rewards. With this, users can get a couple cents at a time, which allows them to "purchase" these books now.
It seems that it used to be possible to register with a generated card number. You can get those for example here: http://www.darkcoding.net/credit-card-numbers/ See How to get Google Music Without Credit Card for Free Music.
Unfortunately I am not able to register a generated card number any more. It seems that Google started to perform additional checks of the numbers.