Looked up total child support i pd in for 2019,Then i'd input it as asked to. It logged me out, said "sign back in" & it'd take me right back where I'd been, but did NOT?

Would the $5,200 I paid in for child support (if it had let me input it into the box instead of it accidentally skipping that step after I had to Re-sign IN again) have lowered the $724 amount I'm having to pay in now?

Yes, when you sign back in the program is suppose to take you to the place you left off.

Child support is not tax-deductible on your tax return.  If you can claim your children as dependents you receive a credit called Child Tax Credit.  If you cannot claim them as dependents you are supporting your children.

Link about Child Support Payments