I'm sorry to hear about your loss. Fortunately, you are not responsible for the debts left by your mother in law unless they were joint debts (i.e. you were a co-signor or guarantor). The debts are the debts of her estate, and if her estate does not have enough money to pay those creditors, those creditors are out of luck.
Yes, you are able to claim funeral expenses, in fact the money for the funeral should have come from the estate, and not you personally unless there was insufficient money to pay for the funeral.
To prove what she has in her accounts, send them copies of the statements along with a cover letter explaining that not enough funds are available to pay the debt in full. If you just ignore the debts, they will seek judgements against the estate but if the estate has no assets, the creditors have no recourse.
Attorney
Negotiate, Draft, and Review many complex commercial agreements each year.