Can you post a picture of the plant?
How bright are the lights, eg wattage vs tank size/ dimensions?
Do you have lots of floating plants in the tank?
These will reduce the light getting to plants at the bottom of the tank.
------------------------
Plants need 8 hours of rest each night so reduce the lighting time a bit. The maximum lighting time you can use each day is 16 hours.
Most people start with about 12 hours of light per day and then monitor the algae growth over the next week.
If you get lots of green algae growing everywhere, then reduce the lighting time.
If you get no green algae growing then increase the lighting time.
If you get a small amount of green algae on the glass, then the lighting period is about right.
Holes in the leaves can be from fish or snails grazing on the plants.
If the leaves are turning brown and becoming soft and mushy, they are rotting.
If the Java fern is new, it might have been grown out of water in a hydroponic system and when you put it underwater, the terrestrial leaves die off and the plant grows new aquatic leaves.
------------------------
Low levels of ammonia and nitrite do not normally cause problems to plants. Really high levels (above 10ppm) can burn them.
The weather shouldn't be an issue assuming the aquarium has a heater in and the water temperature is above 18C (64F).
------------------------
How often are you adding the fertiliser?
Plants like a steady supply of food (fertiliser) and if you add it once every couple of weeks they use it all up in a day or two and then have nothing left for the rest of the time. This can cause unusual growth.
If you add too much fertiliser too often, you can kill the plants.
Both of those products (SeaChem Flourish and Fluval Grow) appear to be trace elements. The Flourish is meant to have iron in it too but doesn't state percentages.
Most aquarium plants do well with an iron based fertiliser added several times a week. You get an Iron (Fe) test kit and monitor the iron levels in the water. You add iron based fertiliser as often as required to keep the iron level at the recommended level (about 1ppm I think it is).
You could try a different fertiliser too. I use Sera Florena, which is a liquid iron based fertiliser. If you could find the ingredients in the fertilisers you use, you could compare it to Sera Florena and see if one has more nutrients or a wider range of nutrients than the others.