As I say, Ive got no personal experience with assassin snails so don't know how sensitive they are, however, if I was in your situation I would either return the snails or find a cycled tank for them, as clearly something is negatively effecting them. If they were this way in the shop, then perhaps something in the shops water was also effecting them (such as traces of medication). When looking to buy snails at the lfs, only go for ones that are lively and moving around
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I would also get rid of that nitrate removing resin, as I think it's probably affecting the cycle in some way. Replace this media with biological media like ceramic rings, or if you want, inert mechanical media like filter floss. The best option for you right now is to get any media from a cycled tank, be that gravel from an undergravel filter or sponge from an internal, and place this in that filter chamber. Any amount of mature media will help at least a bit.
A nitrate remover that "eliminates toxic nitrItes"? Doesn't make much sense unless your talking about an established tank, where some bacteria also convert nitrate into other compounds including nitrite.
As a rule, try to avoid any chemicals that remove nitrogen compounds from your system (
especially when cycling), far more reliable to let bacteria and plants do that.
In mature aquariums, it's not just a simple case of ammonia -> nitrite -> nitrate (this is just the major important process that is often focussed on) but rather there are loads of other bacterial process going on including those where nitrate is converted into other nitogen compounds like nitrite and nitrogen gas.
The bacteria that grow on filter media live in a biofilm - which is like a structured film of different species of bacteria built up in a way so the different species can all get the different foods they require, the important bacteria to us use nitrogen compounds as food..
Anything that removes nitrogen compounds from the system is going to impact on the development of the biofilm on your filter media (the process referred to as 'cylcling'), possibly (as I'd hypothesise in this case) adversely.
Ammolock is probably affecting the cycle in some way too (as it's changes ammonia to another nitrogen compound, that possibly a different species uses), but since it's pretty much necessary to avoid harm to the fish, and it's widely used without adverse effect to the cycle being noticed. So for now take that chemical as the exception to the rule
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