L.R.
I'm so very sorry for your loss -- of course your whole focus was on caring for your husband; that's totally understandable. It is dreadful to have to deal with business issues after a death in the family; I know from experience. I'm really sorry.
But now, please get some legal advice about the estate laws in your state. You may indeed be liable for at least some of his debts. Yes, some businesses will indeed sue over $700. You may need to get a financial plan so you can pay these bills off over time.
Please, please do not let your grief blind you to the point that you end up in a year's time with serious financial problems because you didn't get good advice as soon as possible. If you cannot afford a lawyer, go to your bank and make an appointment with a financial adviser there who has experience in handling estates. Do it today. The bank should be able to help you with the monetary side. And did your husband have health insurance? What if anything does the insurer do about bills for customers who have died? Call them and find out now.
You need solid legal and financial advice NOW, not advice from us here on Mamapedia. You may indeed not be responsible but you need to know for certain.
And yes, as his spouse you will have to file his taxes for him, covering the period since he last filed. He has an "estate" whether you know it or not, even if that estate is one bank account in his name.