2. I am an owner of a flat inside a building that has coverage for third party liability. Can I escape from all liability if visitors or occupiers were injured in an accident inside the building?
If the insurance of the third party's risk only covers the common areas of the building, the insurance company will only pay if the accident happened in these areas (but not inside your flat).
You will have to purchase your own occupiers' liability insurance for coverage of your own flat in respect of injuries to visitors in your flat. Most home-owner's insurance includes this cover.