Can guppies live without an air pump?

No. Cichlids are not fish for beginners and they are not suitable for bowls or small, unfiltered tanks. They are demanding, need good food, and most grow extremely large, with a cichlid considered small if it does not reach more than 8 inches - 12 inches is not an uncommon size for many species in captivity. Fish this large cannot be kept in small tanks - the myth that they will not outgrow their tanks is blatantly false, and they suffer terribly if kept in inadequate tanks. Large fish produce a lot of waste and need good filtration - they simply must be kept in large, well filtered tanks.