As you have no filters, you therefore have nowhere for the beneficial bacteria to grow. This bacteria is needed to break down the harmful substances that are toxic to fish such as ammonia and nitrites. The beneficial bacteria breaks these down and creates nitrates which are only toxic in very high numbers. A filter is where the good bacteria is stored, as in on the media inside the filter. Filters also keeps the water clear for longer and takes out any other substances that shouldn't be in the tank. They also great oxygen for your fish and is also good for plants. They are in short, an essential piece of equipment when it comes to fish keeping.
Please have a read of the "fishless" and "fish-in" cycling threads in the beginners section. Everything is explained a lot clearer there
As for the stock, tetras should be in groups of 6+ but apart from that I have no experience with the other fish you have. All I will say is you will need to be doing 80-90% daily water changes to keep the ammonia and nitrite levels down since your tank won't be cycled. Also invest in a liquid water test kit. This will allow you to see how much ammonia nitrite and nitrate is in your tank and tap water. You can then act on it accordingly.
Good luck