YES. Rocketship makes is easy to upload your own logo and header background image.
YES. Go to the LAUNCHPAD tab and click "Change your site title or tagline..." to enter your tagline.
NO. To change the text and link colors or other design attributes, you will need to build your own custom design (this requires some knowledge of CSS).
YES. This requires a good working knowledge of CSS. Once your custom design is ready to launch, you can switch to use a custom site design from within the DESIGN tab, and then upload your custom CSS and image files.
NO. Rocketship generates HTML and a custom design can only be styled around what currently exists. If you are good with CSS just about any design imaginable can be implemented on Rocketship.