1. I don't recommend that, active email links are actually how most spam bots collect email addresses. Instead, use a contact form: http://en.support.wordpress.com/contact-form/
2. We don't have a direct way of doing this, but you might find what you're looking for at https://ifttt.com/connect/linkedin/wordpress (please note that we don't directly support these ourselves).
3. Even if you set a static front page, the page you set as your blog page will be fully functional, just as it was on the front page.
4. http://en.support.wordpress.com/pages/front-page/
5. Yes, you can fully customize your menu following this guide: http://en.support.wordpress.com/menus/
6. Not directly, but they can be hidden via CSS if you have a Custom Design upgrade: http://en.support.wordpress.com/custom-design/
7. Yes, you'll have to register the blog under that account (visit https://signup.wordpress.com/signup/ while logged in to that account) and export/import the content from the Tools section of the blogs' Dashboards.