There is no form for estimated taxes to file, you would estimate what you owe for the quarter and send that to the IRS https://www.irs.gov/payments
Next year when you file with TurboTax it will walk you through entering all the self employment income and expenses.
You may be able to take a home office if it qualifies here is information about a home office https://turbotax.intuit.com/tax-tips/small-business-taxes/setting-up-a-home-office/L52go3hc0
You can deduct the business percentage of the cell phone and internet
You can also deduct any reasonable and necessary expenses associated with making the income
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