Do I need to file taxes on Mom's income?

If she has filed returns in past then IRS might come looking for her returns, so at the very least, do fill them out and have the forms completed. At some point if the form says 'Do Not return this form to IRS" that only means they don't want to clog up their computers with excess forms, it doesn't mean you don't have to at least complete the forms and keep a copy (which shows zero due) just in case they come looking for it. ("Come looking" in the form of a letter).

probably not, but go to IRS.gov and check to see if she is eligible for tax credits, in which case you would want to file.