The cold no doubt had something to do with your tilapia death. Temps that low will weaken them.
Your new setup is looking good! Watch closely for the ammonia and nitrite spikes, and when they start rising do water changes. The ammonia can affect the plants, too, if it gets too high, so don't be discouraged if the plants are struggling during the cycling.
Carp aren't too picky about light, just be sure they have enough to know night from day. Being indoors you probably don't need anything but your net.
When the nitrates get high, you may see an algae bloom, with algae all through the water and growing on the sides. Since you have plants in the system, it should pass and the water will clear. You can do water changes during that time, too. Don't worry about algae that might stay on the sides of the tank after the bloom passes, as long as it's just a film & not hairy. It makes a nice treat for the carp & lowers your food bill. :)
As for the number of fish, a good rule of thumb is 1" of fish to 1 gallon (4 liters) of water. You can probably crowd it more than that as your fish grow as long as you keep an eye on their behavior and health.