In case you want to connect to another Facebook account, all you need to do is login to Facebook using the other account first, and then go to General Settings where you re-connect with Facebook (this time from the other account).

And yes - you can safely switch between personal & business accounts without any issues.

The account that you'll be currently connected with will be the one that's active and working. When you then switch to another account, that account will be the active account.