I wonder at some filters too.
Does yours have the 'bio-carb' or 'bio-clear' catridges?
The bio-carb ones are meant for tropical tanks and Hagen says they contain carbon and
Ceramitek [which is] a highly porous ceramic biological filter medium, optimizes biological filtration
It sounds from that as though they do put a biological medium in the cartridge....and then tell you to change it every 2 to 4 weeks.
If you do have these cartridges, you do have some biological media so you have 2 choices.
1. Leave them there and don't change them. It's the carbon that needs changing as it gets full in a few days and stops working. But you don't actually need to use carbon. If you leave the cartridges there the carbon will get fulll, but it will also be colonised by bacteria. You will have to be careful if the fish ever get sick and need medication. There is a risk that whatever is on the carbon could get pushed off by the medication and that the med will stick to the carbon instead where it can't treat the fish.
2. If it is possible to make a small slit in the cartridge and empty out the contents, the best thing to do would be, one cartidge at a time, replace the contents with sponge. You would need to wait at least a month before doing another one so you wouldn't loose all your bacteria.
The same choices apply if you have the bio-clear cartridges. They contain zeolite and ceramitek. Zeolite absorbs ammonia, but it too will get used up and stops working. But like carbon, it can also absorb medication.
You say you have ammonia in the water. That builds up first as the fish secrete it, and nitrite won't appear until you have some bacteria to turn the ammonia into nitrite. Then that will build up until you have started growing the bacteria that eat nitrite, and nirate will then start to appear.
Until then, you need to do water changes every time you see a reading for either or both ammonia and nitrite. the water changes should be big enough and often enough to stop either of them ever getting to 0.25. With a reading of 2 for ammonia you need to do as big a water change as you can. Leave just enough water for the fish to be able to swim in. Test for ammonia again after 20 mins (to allow the new and old water to mix) and if it's still above 0.25, do another massive water change.
Four weeks should be long enough to have grown at least some ammonia eating bacteria. It seems unusal that you have no nitrite yet. Can I ask how you are testing the water - strips, liquid tester or the shop does it?
The other thing I'm wondering about is that you have guppies, a dwarf gourami and shrimps still alive. Those fish are notoriously sensitive to bad water conditions and shrimps are usually more sensitive than fish. Is there a possiblilty the ammonia tester is not accurate/not working properly?
Just one last thing - once you have the ammonia (and later possibly nitrite) sorted, you need to look at your fish. You have only one cory and they are shoaling fish. But a 60 litre tank isn't big enough for 6+ bronze cories. Maybe think about part-exing it for a shoal of one of the dwarf cory species - pygmy cories (Corydoras pygmaeus), panda cories, Corydoras habrosus or Corydoras hastatus. Six of one type, not a mixture.