If I paid taxes in April 2019 for the year 2018 ( underpayment)- do I include them in my 2019 tax return? For Federal and State?

No, you do not include any amount of federal tax paid for a prior tax year. Only your 2019 federal taxes paid for the 2019 tax year are reported.

 I am curious about this too. I am in process of filing a 2018 amendment that I own tax on but I apparently prepaid enough to not have to write a check

doesnt that reduce the money I have available to pay 2019?

No. You would include any additional amounts paid for 2018 on your amended return that were not reported on your original return. Doing so may result in an additional refund for 2018. Do not include amounts paid for 2018 on your 2019 return. Each tax year is determined separately.