This is one of the most important and common questions for anyone starting a business on Facebook.
The Simple Answer: Yes, your business page is publicly separate from your personal profile. Your personal information and posts are not visible to your page’s followers.
The two are designed to host entirely different types of content formats; your personal text posts and family photos are kept separate from your professional product images and business updates.
You are correct that a personal profile is required to be the administrator of a business page, but think of your personal profile as the key holder, not the shopfront itself. When you post, comment, or interact on behalf of your business, you must ensure you are acting as your Page. When you do this, your customers will only see your business name and logo, and they will have no way of clicking through to your personal profile or seeing its content from your business page. The separation of your personal and business presence is maintained.
Cheers,
Jeff