Yes, your information will be automatically saved when you sign out or close your browser. TurboTax Online saves your return as you continue through the Interview questions. When you return, click on Take me to my return button, and pick up where you left off to complete your tax return. (See images below).

Yes, you can sign out and your data will be saved automatically. To begin again, sign into your account, then select the 'take me to my return' button. Then select the 'pick up where I left off option'.