Thanks for the extra information, Akiba - this definitely helps to paint a clearer picture of what's going on in there. It sounds like I was on the right track in my first post - you seem to be in the middle of a fish-in cycle with an overstocked tank. Not a good situation, but one that you can correct if you're willing to put some work in. Start with daily water changes to keep the toxins as low as possible and re-home those Balas ASAP.
Fish-keeping is
definitely a hobby in which patience is a critical component for success, as many of us who also started on the wrong foot have learned the hard way. :/
Should the shrimp and snails count towards my stock?
Yes, absolutely! Any living creature counts toward the final stocking numbers.
Each will contribute it's own share of waste into the water column, as well as require enough room to move about freely in the limited space provided.
My understanding is that shrimp are at the lower end of the bioload spectrum, but larger snails, such as the commonly named 'Apple,' or 'Mystery' snail, can contribute quite a bit of waste to a tank.
I read that I can hold 20-25 fish in my tank.
I'm not sure where you read this, but I'm sorry to say that you have been
terribly misled! There are no concrete stocking rules like this one, each fish is unique, and has it's own set of requirements, including space and water parameters, that need to be met in order to ensure their long-term health. I strongly suggest that you do research into any fish before bringing it home, and don't trust information given in a shop.
I really hate to lose the balas as I find them to be quite beautiful but im worried that if i let them loose again they will terrorize the other fish. Could i let the bioload calm down and get two more balas to make them less stressed?
I agree with you in that these are very beautiful animals when well kept, but they are simply not going to thrive in a tank of this size. Sorry to be the bearer of bad news, but again - these fish grow quite large. Unless you're willing to invest in a 125+ gallon tank, you should find them another home. :/
The fish you have now are juveniles, I'm sure. Balas grow to over 35 cm (14 inches) and of course will require much more space than the 60cm tank you currently have. Here is a
link to our profile on these fish. I suggest you take some time to read up on them, and their needs - as well as the needs of the other fish you have. I honestly can't imagine 2 in a tank that size, much less 4 at full growth. . . they would be like sardines in a glass can. . .
I'm not sure what you mean when you say 'wait for the bioload to calm down,' but the bioload is what we use to refer to the amount of wast that any given fish will add to the tank. Some fish create more waste than others. This can depend on their size, diet, and how their digestive tract works, among other things, I'm sure.
The Nitrogen cycle is a process in which colonies of beneficial bacteria form on the surface areas within your aquarium. These help to process fish waste, and combined with water changes, help to keep a system healthy. This bacteria is not yet present in your tank, so the levels of toxins are building up - at an alarming rate, considering your current stocking. This is bringing harm to your fish. If a tank is very overstocked, there may not be enough surface area for an adequate amount of bacteria to handle such a large bioload to colonize - that apart from the bottom line that Bala sharks
can not thrive in a 10g tank. You need much, much larger. . . what you need is fewer fish, more water changes, and a bit of patience while this natural process takes place, and then to keep your stocking at proper levels for the size tank you have, so that the bacteria can do its job.
Also should i replace my plants or will they grow back the lost chutes?
I'd have to see a picture of the damage done, and know what type of plant you have, in order to answer this question. Stem plants, given proper lighting and nutrition, are typically able to rebound.
Last time I asked about a water quality test kit but they told me that I should not worry about studying my water quality this early in my tanks life.
Hmmm... I'm not liking the information this shop is giving you! You
absolutely should be worried about your water quality - I certainly am!
Clean water is required to keep healthy fish - that's just a given. In a newly set-up, freshly stocked tank, the water parameters are subject to
extreme fluctuation. As the fish excrete waste with every breath, toxins build up - and until the nitrogen cycle is established, these animals are running the high risk of losing their lives.
I have no idea what type of testing kits they have available over in Japan, hopefully one of our other members may be able to help you there. Here, the majority of us use the
API Master Freshwater test kit. If you haven't gotten a test yet, I highly recommend you get one. This will allow you to see for yourself whats going on in there, and come to a better understanding of how the process works.
Forgive me if I'm wrong, but it sounds as if you may not be terribly familiar with the nitrogen cycle, beneficial bacteria, and how this process works to ensure the safety of those who live in our tanks.
Here's a link that may help clarify things for you. Give it a read, and post any questions you have. We're all happy to help!
Also if I do have to get rid of the balas after my tank stabalizes could I replace them with some tiger loaches?
I'm sorry! This is another beautiful animal that requires a six-foot tank :/
They're so cute and small when we see them in the fish shop, but these fish will grow to be lager than a foot in length! I have found it to be in the best interests of any fishkeeper to do their research before they walk into a shop, and never take the word of the salespeople there - too often their information is incorrect, and it ends up costing many little lives. . .
UPDATE* I returned today to find another tetra missing, and a hollowed out shrimp. How can I stop losing my stock? And what could have eaten the shrimp? The Balas are still in the barrier. Upon further inspection of my tank I also noticed 5 or 6 new fish. I can tell as they are tiny but they look like new tetras. Should I get a barrier to protect them from other fish?
As stated above, the babies are very likely to belong to the guppies, who are live-bearing fish, and notorious for popping out fry at an astounding rate! Larger fish will eat the smaller, but at this point - though it may sound mean - I would allow that to happen, as your tank is unable to support the fish you have currently, much less any new additions.

Your shrimp likely died from the toxins in the tank, and was picked at by the guppies - who *may* have been picking at it even before it's demise. I've never kept shrimp, but many fish view them as a food source.
I hope this helps you out somewhat. . . you really just need to find a new home for your Bala, increase your water changes, and do a lot of reading up! I wouldn't purchase any other fish for this tank, and were it my tank, I would rehome the Neons, as well. This is the only way that you will stop losing stock.