Q. Since her income is non taxable and I pay the home expenses, I can claim her as my dependent right?
A. Yes. She meets the relationship and income tests. So, it hinges on the support test.
Nontaxable Social security doesn't count as income, for the income test, but social security money she spends on her self does count as support not provided by you, for the support test. Money she puts into savings & investment does not count as support she spent on herself. Note that a parent is closely related so there is no requirement that she live with you at any time, during the year. But if you provided a home it helps your support case, unless they own the home you live in. If no one person (or married couple) provides 50% of the support (for example your siblings are also sending support), then a "multiple support agreement” (IRS Form 2120) can be used, to allow you to claim the dependent. https://www.irs.gov/pub/irs-pdf/f2120.pdf
The IRS has a worksheet that can be used to help with the support calculation. See: http://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf The support value of a home is the fair market rental value, divided by the number of occupants.
Q. Does she need to file a return with her SSDI payments and 1099 income?
A. No. The threshold for filing 1099 income is $1300.
Social security (including SSDI) only 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
