1. If you haven't been sued then you cannot counter sue. You can sue for your medical damages if you can prove those damages were the result of either a) you landlord's negligence or b) a dangerous product (sue the product manufacturer). You should definitely consult a local personal injury attorney about this issue.
2. Your losses due to the fire are your own to pay unless you can show the fire was the result of someone else's negligence. You may be able to recover your food costs if you can show your landlady did not replace the appliance in a reasonable time period. You will need to review your lease carefully for any provisions on damage repair and replacement of damaged fixtures. This would be a breach of contract (lease) action.
3. Generally you cannot live somewhere for free even if the landlord is failing to make necessary repairs. There are certain instances where you can deduct the costs of repair from the rent, but those are very limited and I never advise people to go that route. You can sue the landlord for breach of contract (lease) and seek repairs and damages or you can terminate the lease and move to a new apartment while suing for the costs of the relocation and change in rent.
You really need a lawyer to assist you. These are very complicated legal matters that involve multiple areas of the law (landlord tenant, personal injury, insurance, product's liability, etc). Most attorney will not charge for an initial consultation and may aid you in your initial efforts to resolve this situation.
It appears this matter will require legal action in court.
Please reply if I can help further.