To connect our company's LinkedIn profile, do we have to first connect with a personal LinkedIn profile?

In order to connect a LinkedIn company profile (which is not a user profile), you'll need to go to your SocialBee dashboard, scroll to the bottom, and click on the LinkedIn Company button. 

However, as is the case for Facebook pages or groups, you will need to connect by using a LinkedIn user who is an Administrator of the LinkedIn Company that you want to connect.