you need to do a water change fast if the tetras are in such a bad way. as for that gravel, it depends on whether or not that tank was cycled. many bettas are not kept in cycled tanks.
It'll help only a small amount. Truth is an uncycled tank, for most of our lfs fish, is dangerous and often lethal. Neon tetras aren't very hardy nowadays sadly and the rising levels of ammonia in your tank will stress them and leave them weakened to the slightest disease. Bettas are naturally resilient to tough water conditions as they have evolved to cope with highly depleted and unsanitary conditions in the wild, which is why your betta is fine.
Chances are the neons won't get through this sadly. Let the tank cycle with your betta, but be sure to monitor the ammonia and nitrite levels in the tank and ensure you keep up plenty of water changes until your filter matures.
Things like bio spira (which I have no personal experience of) are supposed to add all the necessary bacteria into your filter straight away supposedly to allow for fully stocking your tank immediately with no ill effects. I have used bactinets on one of my current tanks and with great success. I stocked the tank immediately after setting up the tank and adding the bactinets to one of the external filters and they worked excellently with no rise in ammonia or nitrite in the tank. Although I will add that I have a second, fully mature filter (although small and nowhere near enough for the tank in question) running on the tank aswel.
I'd say right now you can do little more then keep up the water changes and hope for the best. If you do manage to get hold of mature filter material or bio spira or similar then great.
P.
Thank you Miss DD, it means a lot. This is sad indeed, and it's my fault which makes it worse. I'm hoping for the best. I'm going to get a water testing kit as soon as possible and try to find some Bio-Spira or something. What is "bactinets"? Sorry, I'm a failure at this stuff thus far...
Don't feel so bad. We all make mistakes when we first start fish keeping. It's just unfortunate that the fish suffer because of our own ignorance.
I'm in the UK so I don't know if bactinets are available where you are or not. They are manafactured living bacteria that an increasing amount of places are selling around here now to seed filters to allow immediate stocking of your tank. They have a short 'shelf life' even kept in upmost conditions by the stores (My local has said they make next to no money from them as the waste from the bacteria not sold is so high). As with all similar named products they aren't in bottles on shelves. They're usually kept in a specialist machine refridgerated. But they do work. It was about 5 months ago I used them to seed my 100gallon tank which I then stocked with my Malawis and a large family of synos and have had no issues in the tank at all. Obviously the bacteria feed off of the ammonia and nitrite produced by the fish so thrive and multiply over time naturally allowing the tank to mature without all that stressful and tedious mucking about with cycling. And I've cycled a good number of tanks in the past.
On the whole it really isn't your fault as the advice you get from your lfs is what many new to fish will depend upon, and if they tell you incorrectly and know little better themselves, then it's hardly a suprise that mistakes happen and also, sadly, why many give up on the hobby very early on.
Happily on these forums there are very many experienced fish keepers and specialists in every area of the hobby. I have learned a great deal from many of these people myself and can honestly say I wouldn't have the knowledge (nor the amount of tanks!) or skills I have now without them.
Don't lose heart. In the end, all the hard work we all put into our fish is highly rewarded by the obvious happiness of the fish in our care.
P.