Regarding the KHAA:
Sir82 is technically correct. My understanding is that the KHAA is what is referred to as a self insured trust. This trust is a method of financing risk and is typically used by large corporations. There are advantages and disadvantages to this structure and typically (but not always) there will be an insurance policy of some sort sitting above the trust. Its quite difficult for religious organizations of any size to buy sexual molestation coverage due to all the lawsuits in recent years. The intent is to "assist" kingdom halls with their liability and also property claims. I do know that the legal department will issue a certificate of insurance on behalf of congregations when necessary (like when a group of congregations rent a building for a CA/SAD or memorial). Still there duties that insurance companies have that the WTS doesn't take on by financing their risk via a trust as opposed to forming a captive insurance company. Anyway, the unction is still the same to pay claims.
They don't pay taxes because its technically not an insurance company (one of the advantages of running it as a trust)
I seem to remember a case a few years ago in FL ?? where there was an auto accident out in service and the plaintiff dragged the WTS in. I believe the WTS got themselves dismissed because they said the publishers were acting on their own speaking to their neighbors about the Bible (which is a load of crap because the WTS provides the materials, methods, assigns territory to congos, etc). With that being said, had the WTS been found liable for the actions of a member of the congregation (more likely that it would involve elders, MS & pioneers since they are "appointed" by the WTS not by the local congregation), then yes the KHAA is where the money would come from. Although I don't have first hand information, I'd bet my house that's where the settlement money came from.
I know of situations where there was a claim involving a person who fell on KH property and they were going to bring action against the congregation. There is a form that each congregation has to complete and send to the legal department when something happens at the KH. Pretty standard stuff for a large corporation with mulitple locations.