Does my 16 year old dependent have to file taxes if she receives SSA and works part time? What are income requirements for filing?

She does not need to file. 

You do not report his/her income on your return. If it has to be reported, at all, it goes on his own return. If your dependent child is under age 19 (or under 24 if a full time student), he or she must file a tax return for 2018 if he had any of the following:

1.         Total income (wages, salaries, taxable scholarship etc.) of more than $12,000 ($6350 in 2017).

2.         Unearned income (interest, dividends, capital gains) of more than $1050.

3.         Unearned income over $350 and gross income of more than $1050

4.         Household employee income (e.g. baby sitting, lawn mowing) over $2100 ($12.000 if under age 18)

5.         Other self employment income over $400, including box 7 of a 1099-MISC

 Even if he had less, he is allowed to file if he needs to get back income tax withholding. He cannot get back social security or Medicare tax withholding.

In TurboTax, he indicates that somebody else can claim him as a dependent, at the personal information section.

Note that social security benefits are not mentioned. Social security only becomes taxable when added to sufficient other income. If she is otherwise required to file a tax return, you do need to enter it in Turbotax (TT). TT will determine the taxable portion.

Social security (including SSDI) becomes taxable when your income, including 1/2 your social security, reaches:

Married Filing Jointly(MFJ): $32,000

Single or head of household: $25,000

Married Filing Separately and lived with your spouse at any time during the tax year: $0