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If your dogs ate the pills within the last thirty minutes, I would immediately feed her 1 tsp per 10 pounds body weight of 3% hydrogen peroxide to induce vomiting.
The dosage of methadone that we use in dogs is 0.2-0.3mg/kg bodyweight, so unless your dog weighs over 100 kg, she has had a large overdose. If you don't have hydrogen peroxide, or it doesn't induce vomiting (it doesn't work in all dogs), I would immediately take her to your nearest emergency vet for treatment.
I cannot say. The methadone depresses the respiratory drive, so she will not be getting enough oxygen. Explain the financial situation to them, or call vets from the phone book and find someone to treat her on a payment plan. I know this is a hard situation for you.