I can help provide some information about using a third party program in tracking sales and payments that will sync into QuickBooks Online as well.
If your client is using a third party app that works with QuickBooks Online then yes, you can automatically import the transactions from that application into QBO by integration. To check if this is compatible, you can refer to this link: How do I find apps to connect to my QuickBooks Online?
If you can find the third-party app on the available list, you can contact them for help on how to integrate the two programs.
I'll chime in this thread to assist you in paying the sales tax in QuickBooks Online (QBO).
From the information you've provided, it sounds like your client is using a third-party software to track sales and payments and they want to manually enter and electronically pay the sales tax in QBO.
If this is the case, there is a feature to electronically pay and file tax liability and returns directly in the QBO account. However, the sales transactions should be manually entered to be able to use this feature.
The detailed steps can be found in these articles: