There are some benefits to buying from a used car dealership versus private. Buying a used car from dealership means it will come with a warranty for a certain length of time, it also means you can go and test a large number of cars in the one spot.
One word: depreciation, when you buy new car it loses a large amount of value as soon as you drive it off the lot. By purchasing a secondhand vehicle much of this depreciation has already occurred enabling you to pay less than buying a new vehicle.
Yes, you can have a used vehicle you are interested in checked by your local NRMA or equivalent organisation for a fee. If you have a mechanic they will also be able to offer this service.