Is there a type/brand of birth control that doesn't or barely protects against pregnancy? can you still get pregnant on it?

Nothing is perfect: But most common reason for contraceptive failure is due to improper use. All approved contraceptive medications and devices are very effective (greater than 90% effective when used properly). Reference: http://www.Nhs.Uk/conditions/contraception-guide/pages/how-effective-contraception.Aspx some have higher failure rate because they are more prone to improper use. That is the main factor.