It's not the night of the living hydroids taking place here... those things are not killing your fish.
There really seems to be some kind of Illness taking place... Ich will typically be noticeable long before it results in death. Especially in hardy fish like clowns, they will often times survive through multiple cycles of ich if not beat it altogether. But it really sounds like you have some sort of parasite or pathogen in your tank introduced by one of your fish.
Now of course it is not recommended to have a glass top covering your tank and you could be low on oxygen. So remove the top regardless. Unless it's a sump system then you may be fine with keeping it if your sump is not covered and you have really good water flow or you have a big enough of a gap on the lid and it's not 100% covered. If it is an oxygen problem you will probably have seen your fish breathing heavily fairly quickly after introducing them and never stop until they died
The white spots u mentioned sure sound like ich but keep in mind there can be a presence of ich and fish may not even contract it simply due to being healthy and having a good slime coat... and if all of your fish aren't breaking out in white spots and they're still dying you probably have something else going on that reduced the fish's immune system and made them more susceptible to ich so you just happened to see that sprout up as well.
But I'd say that you are not likely just buying all, already sick fish, unless all of them were together already in the same tank and being subjected to whatever disease is likely taking place here.. That being said if the LFS's same batch aren't dying but as soon as you put them in your tank there are problems then the disease is probably in YOUR tank now and by adding new fish, healthy or sick whatever... you are providing a new host to keep it going. Typically diseases don't affect fish and inverts the same so your inverts should be fine to leave in there but you need to keep your tank fishless for a period of at least 6 weeks. Regardless of what disease or parasite you may be encountering here Beth's advice is going to be the best to get rid of whatever's in there. Sucks.. you probably don't want to do that because you want stuff in your tank but it's really better to be safe than sorry. Don't let it deter you or get you down... just take the necessary measures to get rid of it then start adding live stock again.