Why is a minor child required to pay taxes

My child is 14 and work for family company. I issued W2 of $6250 for her contribution. By IRS rules, I do not need to hold any SS tax, medicare tax, or FUTA tax.

 

1) When I was issuing the W2, Turbotax constantly told me that Form 941 is not consistent. As a result, I ignore the warnings and it should be OK.

 

2) When I am filing the tax, Turbotax warned me multiple times that the kid will received a W-2c form.  The information is like ... "since you deferred some of your social security taxes last year, you will get form W-2c from your employer once you've repaid what you deferred."...

I am totally confused with the above warnings.

 

3) NY is charging the kid $125 tax. Should state tax be zero as well for minor child?

 

Thank you very much for your help.