I bought my house at 2018 and I refinance it on 2019. So I getting 2 1098. Should I combine that as a single entry in the deduction or enter as 2 separate entries?

You should enter both Form 1098's in separately. The software will combine amounts on the tax return.

What figure should I enter in outstanding mortgage balance for the original mortgage? Since the original one is paid off, the balance should be "$0" but, when I enter $0 in TurboTax, it doesn't let me go to next step. Please advise. Thanks.

On the screen that says, "Let's get the details from your  1098" at the top you should enter the information printed on your 1098 form. Box 2 asks for the Mortgage balance on 1/1/2019. 

You need to enter each 1098 form and deal with each loan separately. 

A few screens later, it asks you whether you paid off the loan, or refinanced it during 2019. If you answer, Yes. It never asks about your mortgage balance again.