You would normally required under the terms of any tenancy agreement to replace any of the landlord’s fixtures and fittings which are beyond repair. That would include the lock.
So the chances that you are actually responsible for this. Some landlords will replace the locks because they want to be in control of the keys but I would be very surprised if it was the landlord’s liability.
If it is the landlord’s liability, and he will do it, then you have to do it yourself, pay the bill, and then pursue him for the cost thereof, through the Small Claims Court is necessary but you cannot withhold rent or otherwise you will be in arrears.
There is no heating or hot water, then you need to complain to the Environmental Health Department at the local authority and ask him to declare the house unfit for human habitation.
Similarly, with the infestation but if the mice existed before you moved into the property, then it’s the liability of the landlord but if they featured after you moved in, then the liability is yours although generally, the local authority provide a lot of assistance.
Can I clarify anything else for you?
I am happy to answer any specific points arising from this.
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