No, as a dependent your standard deduction will be your amount of earned income + $350 up to a maximum of $12,550.
Even if your deduction wipes out all your income, you will still be responsible for paying your self-employment tax. As you said your self-employment tax is 15.3% of 92.35% of your SE income. This does not include your W-2 income. Self-employment income is generally reported on a 1099-NEC, but depends on the line of work that you are in and how your income is received.
The amount you see on Schedule 1 for the deduction of half your self-employment tax is done behind the scenes when you reported the self-employment income. Same with the tax reported on Schedule 2. If you do have self-employment income, the amount of income can be reduced by any ordinary and necessary business expenses that you incurred to generate the income. Be aware that if you start including expenses and your total earned income drops below $6,000, you will no longer be able to make the maximum Roth IRA contribution.
