No, the NM CRS-1 payments were to New Mexico and would be for estimated income tax payments for the state. These payments should be entered in your federal return as estimated tax payments and they will be deducted from the amount you have due to New Mexico.
Self-employment taxes are the Medicare and FICA taxes due on self-employment income. If you were a W-2 employee, then the employer pays half the FICA and MCare taxes and the employee pays the other half. But self-employed business owners pay both the employer and employee portions (total of 15.3%). This is a FEDERAL tax and can be paid quarterly, along with federal income tax estimates using the 1040ES forms.
TurboTax will determine the amount of self-employment taxes due for your business for 2018 and include it on your federal return. Therefore, if you have any income taxes due on your federal return, the self-employment tax amount will also be included in the total due.
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