Whether you are buying or selling you will get involved in conveyancing, this is the legal part of transferring ownership of a property from one entity to another. When you buy a property there are contracts for the sale, for the mortgage the legal work to create and check these documents is called conveyancing.
Yes, most of use are not legal experts so when it comes to doing a large purchase such as buying a property it pays to have someone looking over the documents who is well versed in the laws related to the process. They can guide you and help ensure that you don't end up in a bad position.
Sooner the better. If you are interested in selling your home you should contact a conveyancer to start the process. If you are buying a property and have found one you are interested in you should contact a conveyancer before you make your offer on the property.
No, property laws vary on a state by state basis. Your property conveyancer will be well versed in the laws and systems that exist in the state they practice in.
Property settlement is when all the pieces of the property buying or selling all come together. The banks will exchange the funds and the titles will change hands.