Can I file for an extension from the program I bought and installed on my computer? If yes, how? Or can I file from the website though doing taxes on computer?

You can prepare an extension for mailing with the desktop version of TurboTax, but you cannot e-file a extension.  We suggest that you file your extension by e-file using our free online service.  https://turbotax.intuit.com/irs-tax-extensions/