Yes, you can deduct the miles driving to your students' homes as business mileage. This is an expense which will be deducted from your 1099-MISC income. The amount you made on your 1099-MISC does not matter, as long as the mileage is real and reasonable.
Estimated taxes are taxes that you voluntarily pay to the IRS each quarter to cover income tax and self-employment tax and income tax if you expect to owe more than $1,000 when you submit your return. If you have another W-2 job and have federal and state tax withheld, you do not need to pay estimated taxes if you expect your 1099-MISC will incur less than $1,000 of tax. You can also fill out a new form W-4 to ask your employer to withhold an additional amount of tax from each of your paychecks to cover the tax on your 1099-MISC income.
Please read this TurboTax aricle on Estimated Taxes:
https://turbotax.intuit.com/tax-tips/small-business-taxes/estimated-taxes-how-to-determine-what-to-p...
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