I've kept fish and aquariums as a kid, but nothing this big. It's never had fish in it, but I suspect that plants and fish could be the key. Let me explain:

The feature is roughly 4000+ litres.
It was built as part of the house, and has a concrete, rubber lined and rock covered surface.
It has a BIG pump (to power that waterfall) and a swimming pool filter.
There is a large skylight above it

After a few days running it, there is scum and foam appearing. A local swimming pool guy tells me its probably because of years of built up micro-ogranisms and proteins. He gave me SPA defoamer, which I used but I know thats not a good long term solution.
There is NO bio filter - just the pool sand filter, and some rather bizzarre plumbing.

I think I need to stablise the water before I introduce fish. I have a limited budget (Hey! I just bought the house) and I'm looking for approaches to make this work. The past owner gave up I think - but I don't think they were game to take the step of adding lil\ve plants and fish (they just added BLEACH to keep algae under control).

There have been some awesome advice given here - any takers for this one??

Foam could be what the pool guy said, search "dissolved organic compounds" (DOC) for more info. Then again it could have been soap someone left in there. An experienced person can tell the difference.

Your current set up is meant to use BLEACH. I assume the use of caps means you think chlorine is evil? I can tell you this, messing around with a pond in the backyard people can afford to not really learn very much and just try different things. It's all for fun. A water feature inside the house is a whole other ball game. Those light smells you get off a backyard pond once in awhile...inside a house can make the home unlivable. So this is a good time to really consider all aspects with a scientific mind set and not a Larry the Cable Guy mind set.

No fish.
The easiest approach is to not have fish. Chlorine is used to kill algae and you can use normal spa or pool chlorine but you want to keep the levels as low as possible to reduce odor. The small amount of sunlight in a house helps reduce the speed of algae reproduction so not as much chlorine should be needed. There's no difference in keeping a spa or pool and an indoor chlorinated water feature.

Without fish you can empty the feature as often as you like for cleaning. All depends on what you want.

It sounds like you're thinking of adding fish and plants to solve the foam problem? Unless you want fish I would not add fish or plants. They would produce more DOCs, not less. Foam is easy to handle. Drain the feature and refill. Repeat as often as needed. Or search for "protein skimmer". The water can be used for outdoor landscaping so no waste. And that's the best thing you can do, create a set up to make it easy to use the feature as a source for outdoor watering. The feature would always be getting fresh water.

Fish.
If you want fish you will still need to do water changes often. There's really no difference from the aquariums you kept as a kid. No glass to clean is about it.

Your feature would be able to convert ammonia from the fish without any kind of add on biofilter if you don't add too many fish. Nitrifying bacteria don't know if they're growing in a biofilter or inside the water feature. They're happy either way.

Plants, including algae, can remove nitrogen but you will be limited by the kinds of plants you can use in low light. Search for "nitrogen cycle" for more info. Less light means less growth, less growth means less nitrogen use. Nitrogen isn't a big concern and water changes would handle that.

My plan is to have an outdoor pond connected to the indoor water feature. That would handle the nitrogen issue.

Sand filter.
Whether fish or no fish you can use the sand filter. It may need more cleaning with the fish because you'll be tossing in food. You do want to make sure there is some kind of strainer basket to keep the big stuff out of the filter.

I think a sand filter in either case is overkill. Pretty expensive in both electric and maintenance. I'd consider dumping the sand filter and using a much smaller pump. Depends on what kind of movement and sound you want.

Other choices.
At some point in the future if the set up is just too much work you might consider filling the feature with rock and planting pond plants in the rock. The water is kept below the surface so no algae and you don't see the bacteria systems most people don't like. This can be a very modern look and give you just a hint of earthy smells in the house. This also allows you to scoop out pockets and have little mini pools in the feature, even with fish. You get to control how much exposed water. Once very 5 years or so the feature would have to be cleaned. You'd need to set up a lot of serious ventilation because the odor would be bad during the cleaning.

Another choice is add the rock and plant normal plants in pots and water as normal. Same basic look.

What kind of lining breaks down and foams?

The next time my DH mentions moving his aunt's unused, garaged car because the tires are deteriorating, I'll be sure to tell him rubber doesn't deteriorate.

The 20 or 25 year warranty on EDPM is based on losing 1 mil per year to UV. That's the only thing I know of that damages it. For roofing UV is an issue. Obviously if it's kept out of UV there's no data on how long it would last. Wouldn't surprise me if it lasted 500 years.

Sorry if I misunderstood, I thought you said "foam sounds like it could be from a deteriorating lining."

sigh...Since actual rubber is used less and less while synthetic rubber is used more and more, terminology gets more and more confusing. EPDM is a synthetic rubber. While some tires contain rubber, synthetic rubber is becoming more common. There are any types of synthetic rubber. They are primarily petroleum products. I don't know why it is called rubber except it was developed as a replacement for natural rubber which is a very limited resource. All of it is subject to deterioration although isolation from chemicals and UV will extend it's life substantially. The water feature in this post was not filled with water for four years. So it has had more exposure to chemicals and UV so there is likely to be some deterioration. We don't know a thing about the water that is being used which can make a difference. Was the sand in the sand filter replaced? The guy who suggested the spa cleaners probably has a good idea but I have heard all sorts of complaints about those.

I could come up with all sorts of things to check out but the easy fixes should be tried first and given some time. If it was my project, I would get rid of the sand filter first and have the water tested.