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.
No you cannot read them with out providing your credit card details.
You have to provide them or use Google Wallet.
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.
Simply, No you cannot.
A sad fact really, as many youngsters want to read through their phone and this limits many to do so.