Ok, that info is all helpful.
First off, if I were you, I would never return to that pet store again, as that person has no idea what he's talking about. He's trying to treat a pond like a tank in a house, and they are two very different things. RUN, don't walk away from that place.
Second, you do not NEED snails in a pond. In fact, I hate mollusks in a pond because if a snail dies, it can take a long time to figure that out and the corpse is rotting and polluting your pond.
You NEED to do a 20% water change in your pond EVERY week--particularly in a small pond such as yours. It is much harder to control water quality in a small body of water versus a bigger one. I would start with a 50% water change right off the bat since you have murky water at the moment, and then do 20% every week thereafter.
You have too many koi in a 500 g. pond. Not even 1 koi belongs in 500 gallons in my opinion. Yes, they are little fingerlings when you buy them, but these are animals that grow to 18-24". A pond of your size is a watergarden and should have a few comet goldfish if you like.
In your third picture, why is your basket upside down. Are you doing that just to keep your media down? I think you do not have enough media in that bucket, first of all. You need much more stuff in there. It should be filled nearly to the top. Why is the bucket in the water and not out of the water. You are taking up valuable real estate in the pond with that thing in there. It also looks unattractive (I am married, and the wife, so I can fully relate to what you are saying! LOL!). Let's make things more attractive.
A UV will work, you don't need a very big one for your pond. You can probably pick up an 8-10 watt one on ebay pretty cheaply. However, if you aren't doing water changes and keeping up water quality, no UV.
You need to solve several problems:
1) you need to cover your pond with a net in the winter so you don't get leaves decaying in the pond and therefore, litle to no muck
2) you need to change up your 5 gallon filter and get it out of the pond
3) as hard as it is, i would rehome some of your koi. you have too many for pond.
4) Get rid of that crap filter, and perhaps do a 10 gallon bio/mechanical filter in one. I will give you some links for ideas. Hide it well, so the wife approves.
5) you can get a UV once all these other componenets are in place.
