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.
How to get your support tickets resolved faster
Statistics have shown us that the more you tell us when you report an issue, the faster we solve that ticket. So...
1 - If you have screengrabs, please include them. A picture is worth a thousand words.
2 - If you have recorded a video showing the issue you're having, please include that as well. A video is worth a million words.
We recommend a free service called Loom for creating these videos. (this is a link to https://www.useloom.com/)
3 - To speed up ticket resolution, follow these useful tips How to Write the Perfect Support Ticket (That Gets Results Fast)