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You should grow a Venus fly trap in a peat moss and sand mixture, which will provide mild acidity and help hold water without keeping soils too soggy. So, the sphagnum moss should be a part of the potting mix the venus trap resides in.

For more information on the care of venus fly trap, please visit the following link:
https://www.gardeningknowhow.com/houseplants/venus-fly-trap/venus-fly-trap-care.htm

I am not entirely sold on the idea of using the tray method for venus fly trap germination because I think you run the risk of saturating the potting medium, which in turn could rot the seed. I would pursue this method of watering perhaps later on when you have a more established plant. I would also suggest starting off your seed in bright indirect light versus putting it in direct sunlight.

For more information on growing venus fly trap, please visit the following link:
Place your germination chamber somewhere with bright indirect light.

The insects may not be triggering the closing mechanism. There are three hairs inside each trap. For the trap to close, at least two of these three hairs must be triggered. Look carefully along the midrib of the leaf and you should be able to see the hairs. Additionally, the traps may become inactive if triggered too many times. A single trap can only open and close a couple of times before it will no longer function.
Also, these plants respond best in full sun or bright light (for at least 4 hrs a day), so make sure your is receiving adequate lighting.

Finally, VFT have a dormancy period of which they will not "eat" anything.

Each trap will normally die after it has digested a few flies, and the plant will grow a new trap to replace it. However, if all the traps turn black at once, this could be a sign of trouble. Overfeeding (too many flies caught at once) or addition of fertilizer (Venus fly traps do not need fertilizer) can cause this as these can be sources of stress.

Venus fly traps can have difficulty in a terrarium for several reasons. One is that terrariums can get hot inside (by the greenhouse effect). They also need soil drainage to prevent root rot, but a terrarium that has drainage holes in the bottom can take care of that.

Venus fly traps do need some humidity, but it can also get excessively humid inside a terrarium, so if you do grow one in a terrarium, make sure there are ventilation holes in the top.