1) The tank appears to be overhanging whatever it's sitting on. You need to fix that by placing it on something larger or using a 3/4 inch sheet of plywood under the tank that's the size of the tank bottom as overhangs can stress the tank seams and cause leaks/cracking
2) The fish DO need a heater, set to around 25C. The previous owner maybe had a warm house and got away without using one, but it's not good for the fish.
3) The tank needs filling up to the top - the fish need the depth for swimming room and territory.
4) A dechlorinator for new water is essential - the filtration relies on the growth of beneficial bacteria that convert toxic ammonia from fish waste via slightly less toxic nitrite to mildly toxic nitrate which you then remove with water changes. Tap water contains chlorine or chloramine to kill bacteria that could be harmful and will also kill the bacteria in your filter leaving fish at risk of poisoning.
5) If the only filtration is the filter on the left of the image, it may not be adequate for these fish. Can you post the make/model so we can assess its suitability?
6) Malawi cichlids like these need a good deal of rock work in the tank to create caves and crevices they can hide and spawn in. This also reduces the risk of damage to any one of them from aggression by the others.
7) If you put the length width and height of the tank into the Tank Capacity calculator on the right of the page it will tell you what the tank volume is. This will help in working out whether or not the filter is adequate.
9) It's important for these cichlids to have hard alkaline water so check your tap water hardness and pH on your water supplier's website and let us know what they say. You need to look for the page on water quality and then enter your postcode into a box that will generate a full report for your postcode area which includes hardness and pH.