I appreciate you for performing the initial steps to help resolve this, @Nevarc76. 

It's good to hear that the program is calculating your new employee's federal tax after changing their dependents to zero. 

We always want to make sure we're compliant with the federal rules and regulations. Per the IRS, taxpayers can no longer claim personal or dependency exemptions. Yes, it's possibly correct based on your first question above. For more information, go to Page 2 through this link: Publication 15 (Circular E), Employer's Tax Guide. Then, locate the "Redesigned Form W-4 for 2020" section. 

I'd still suggest consulting your accountant or tax advisor for further guidance about your employee's withholding. 

For your second concern, we want to ensure that the product is deducting payroll taxes accurately. Thus, you can check out our guide to learn more about how QuickBooks calculates them. 

Also, I recommend visiting this website: Federal W-4. It contains more details about the new changes to the form and how to enter and print it for your employees.

In case you need to manage your payroll and keep track of employee expenses, run and customize reports in the program. Just go to Reports from the top menu and select Employees and Payroll.

Feel free to drop a comment below if you need anything else. The Community and I will be here to lend a hand.