2. Yes, she has demonstrated that she is likely to be a "public charge", read this carefully http://www.uscis.gov/green-card/green-card-processes-and-procedures/public-charge
3. Depends on where the money county pay out of, you might or might no be responsible
You signed http://www.uscis.gov/i-864 , did you not? On page 7 of 9 of http://www.uscis.gov/sites/default/files/files/form/i-864.pdf it clearly listed what program you are responsible for reimbursement, and which program you are not responsible.