I have a fountain in the middle of a 9ft diameter pond, but no water filter installed. If I want to add say just goldfish (or similar type fish, I'm definetly not into Koi carp etc.) to the pond, do I need to install a water filter as well ?
Not for them to survive, no, but if it help keep the water clear so you can see them .yes.Goldfish tend to grow bigger depending on how big there environment is so watch it, they could grow. I'm no expert BTW, just had a pond some years back and had goldfish and shubunkins in it.
It depends how many fish you put in the pond. If there is no filter then the pond plants must digest and neutralise the fish waste and other biological detritus eg dead leaves. The pond will need to be heavily planted and you should put only a few hardy fish in. You could buy a cheap pond test kit and check on the water quality before you add any fish.
how deep is the pond you will need at least 18 inches in a ground level pond more in a raised one so it doesn't fully freeze in winter if you want to keep goldfish so long as you have about half the surface covered with floating plants or lily leaves it should stay fairly clear too