I have an account with twitter, which I mainly use for basketball and a few other small things.
Twitter basically says that they collect information through many different venues. Through: Widgets, apps, sms, tweets, ads, etc., they collect and are willing to share most public information such as: Name, e-mail, location, picture, etc., with marketers and the government.
If the company goes into bankruptcy, a merger, or the company is sold, your information will be sold with it or to another company.
If you use commerce services through Twitter, they will obviously share that information with the necessary third party service providers. They do consider credit card information and shipping address private and will not share that information publicly, but will store that information on their database.
Basically, Twitter will share all of your information, with the exception of Credit Card information and shipping address.