You should only make them quarterly. Put the amount you want to pay each week in a savings account and then take it out quarterly to pay the estimated taxes to the IRS. For 2020, you are not required to make your first two quarterly payments until July 15 although you can make them earlier if you want to.
Yes you can make a second quarter payment by July 15 for taxes you think will be owed based on your 2nd quarter income.
You can use the TurboTax TaxCaster to help you decide how much estimated tax to pay: https://turbotax.intuit.com/tax-tools/
Don't forget your state taxes if you have a state income tax.