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.
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.