Hi there,
The water parameters that pet store employees think are okay, and what are actually okay are very different. If he was willing to bet money on ammonia being the cause, it means your tank is not completely cycled yet and there was likely an ammonia reading. In that case he lied - ammonia reading should be 0 and anything above is not ok.
Not sure if you know about the cycling process if you are new to aquariums, but it is basically establishing a colony of GOOD bacteria inside your tank (mostly in the filter media (sponges, etc)) that break down Ammonia (very toxic) into nitrites (somewhat toxic) into nitrates (not toxic unless levels get too high). The way you cycled was, to be honest, not a good way to do it. But, many many many of us have been there and made the same mistake. Anyways, the fish produce ammonia as their waste product. If you do not have a bacteria colony established in your filter system yet (I believe somehow this beneficial bacteria is in the water and establishes itself in your filter), the ammonia won't be converted into nitrate and will stay the toxic ammonia. This causes all sorts of stress and makes your water quality very poor which can weaken fish's immune system and if ammonia is too high can actually kill the fish from ammonia poisoning. So, that's the cycling process. You did it by adding fish and their ammonia probably sat there with them for a while until the bacteria colony slowly developed to take care of it. After a month the cycle should mostly be done especially with a cycle with fish. So anyways, that's basically why your fish are probably sick. Your tank was not cycled when you added fish and the build up of ammonia lowered their immune system and caused them illness.
How can you lower the ammonia and improve water quality? Many water changes. It might be best to go and get your water tested again and write down the exact numbers and post them here. We can tell you if your ammonia, nitrite, and nitrate levels are okay or not. But anyways, ways to ease the problems associated with a non-cycled tank is through plenty of water changes. I'd maybe do 35-50% water changes every few days until your fish start to get better. You may also want medications if you can post pictures and we can diagnose the diseases?
I just reread your first post and I gotta tell you.... be skeptical about the advice the pet stores give you. As i mentioned. What is "good" to them is usually somewhat far off from what is actually good. Also they will try t sell you stuff to fix PH, nitrates, nitrites, ammonia, etc. And when everything is done properly you will not need any of those, and they can actually be more harmful than helpful.
On another note, your tank is a bit overstocked. Mollies are quite big for a 60 L tank, and there's just too many fish. I suggest picking out a few of the ones you really like and we can help you get a good stock level. Your tank will get dirty fast and the fish will probably be stressed and over crowded if things continue. I'd return some to the store or give them away. I don't think they will lead healthy lives (if some don't die off) if kept the way they are.
Lastly, I'll go a tiny bit into plants. I assume you probably haven't bought any proper lighting for the plants, and the ones that typically come with fish tanks aren't suitable for plants. You might want to check the kelvin rating if you can. 6500-6700k is usually good. Your plants will probably die unless you get light bulbs with kelvin ratings of 6500-6700. This is likely why the plants are dying.... Bulbs are not too expensive and might be worth the investment if you wish to keep your plants alive. Also, "big leaf plants" and "Grass" plants are LIKELY heavy "root plants" and should not be disturbed once planted.
Sorry about all the random stuff, but I'm just spewing out random information I guess that might be helpful because it is 5:57 AM and I'm a bit tired and don't wish to edit it all up.
Good luck with your fish, and if you have any more specific questions or need help with anything let us know, I'll be glad to help with whatever I can.
Btw, don't worry, you'll get your fish tank nice and running smooth soon especially if you listen to our advice here. ^^