yes live plants will be great, it will increase the likeliness of your fish because it give more natural feeling to them. So it will be great and it will keep balance of chemical some plants can do that. So choose right plant for your tank.
May be your fishes doing all this, some fishes like goldfish are very messy so they do all such kind of things or just increase the level of sand so that your plants can be much secure.
Its very common and annoying problem of having algae in the tank. There are many way to prevent them, you can use some good chemicals available in the market or you can have some algae eater fishes in your tank.
Nice pond buddy, you have posted pictures very nicely from the start of the construction of it. so really good work. And I have seen fishes in your tank. All are very nice.