Someone said these smaller ones are harder to keep from getting green and keep clean. They are correct. Think about a kiddie swimming pool as compared to a big in ground pool. The kiddie pool has to be cleaned daily. However, a small pond like yours CAN be maintained to stay fairly clear and pretty. I have the same one you do. Here's what I do:
A few things come to mind. Your pond form looks exactly the same as mine (50 gallon kidney bean). It appears that because you have it buried all the way it is filling up with a lot of grass and other vegetation and dirt that is going to continue to get rotten and feed algae like guests over for steak dinner. What I did with mine that really is a GREAT help in keeping that stuff out without having to use a net covering it (and marring the beautiful view IMO) is I only buried it halfway (up to the underside of the shelf ledge that is on the one side, yours probably has that but i can't tell). And i lined the exposed walls with decorative slate rock. What this does is it keeps out a LOT of vegetation and dirt from falling over in it. I rarely have to skim a lot of junk out.
Secondly, with zero plant life in there you have nothing competing for the oxygen that the algae needs and wants. YEs, it is a small pond, but you can easily get to scale plants. I have 50% of my surface covered in plants and I know that has helped keep algae blooms down. The water is fairly still except for the side where the waterfall rushes in, providing a nice oxy burst. but for the remainder its kinda still so that my mini water lillies are flourishing. they are growing great and providing a lot of shade. I also have a pot of mini cattails in there and in the shelf ledge I have two other marginal water plants. I have anacharis growing in various places directly into the gravel on the bottom, and floating hyacinths. My goal with all the greenery is to keep it getting most of the oxy that the algae wants.
I also see that in the first pic it isn't even full. Maybe that was a temporary thing. But do keep it much fuller than that because with a 50 gallon pond or around taht size they are already shallow, so you want to keep it topped off as often as it needs. Since I live in the city and have chlorinated water I just keep a five gallon bucket full near the pond that I fill up each time I have to top it off. 24 hours of sitting in that bucket naturally gets rid of the chlorine w/out having to use a chlorine remover.
My next suggestion - I know you are using a bucket filtration system, and that is a good idea, my waterfall is similar to that. I have a good layer of rocks in each section and the water hose goes directly into it so it creates a nice filter, but in addition I have a mechanical/biological box filter I bought from lowes that really works great for this size pond. It is good enough for up to 200 gal's so you can imagine it does well for 50. I only paid about $30 for it. It consists of a rectangular black box (not too big for this pond) and you put your pump directly in first. Surrounding the pump is good bio media, then two layers of spongey filters - one finer grained then the other. Then you put the top on which is vented to allow debris in for filtration and a hole in the center for your tubing going to the pump. It is mechanical, however, also biological as bateria grows in the sponge filters (its more like ac filter materail than really a sponge) and the bio media in the bottom. This system has worked well for every small pond I have had. In conjunction with the gravel filter I've had good results. If you are interested I am sure I could google up a product pic for you. If you wanna save bucks it would also be easy to make, i just enjoyed the convenience of buying it already set up.
I also have a small bundle of barley in mine so that it keeps a good balance as it decays it puts out an enzyme that helps fight algae. I think it is called an enzyme, let's just say as it decays it is good for algae prevention. If you use it, you don't need a big bail just a small bundle in netting and keep it where there is good oxygen in the water.
Last, I dunno but that looks like a lot of fish for such a small pond. I have four med size goldfish in mine and that seems like a good balance, I could probably have more but dont want to over stock. I think you have quite a few in that small pond. Like i said I am not 100% sure but I think thats a lot of fish for a small pond especially since you have no plants in there to offset the balance.
I hope this helps. These small ponds can be a nightmare or a joy. I have been working hard to keep mine a joy however I have had larger ones so I have had some experience with trial and error.
This all sounds like a lot but it isn't once you get the hang of it it takes no time at all. Getting this stuff done when setting up is the hardest part and should IMO be considered as a natural part of pond set up. Setting up better in the beginning will make for less heartache and labor on the pond regularly later on. If you do these things you can probably shed that white liner and go back to a more natural looking set up. The algae that grows on my walls does NOT make the water look green at all. It gives it a nice patina that makes it look more natural. I think you just think the side walls are making it look green. That pic you showed of the white liner - that green muck looks like way more than just green side walls. You can better tell if it is the water or not by scooping a cup of water out of your pond in a site cup. IF the water looks greenish, then its the water, not just the walls.
Good luck!!!!