Selaginella apoda is not a moss. It is a member of the plants that are called fern allies. In Europe the commonest member is probably Selaginella helvetica which I believe occurs as southward as Italy.
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S. apoda is a creeping plant that spreads out along the ground though it can have branches that rise up a little into the air.
The plant should be grown outside only. It can grow with some sunlight during the day but recommend only early morning or late afternoon sunlight. It loves humidity and a mosit substrate but not a wet one. Spray it at least once daily with rain, distilled, or r/o water only. If your weather is hot and dry then you should water every two to three days and spray at least twice a day.
You may want to put the potted plant inside an old fish tank or something similar to help keep the humidity up but do not seal shut as it seems to do better with some air circulation.
My climate should be similar to yours as I am in coastal California and we tend to have a Mediterrean type climate here. My plant grows as a weed in some moss and is exposed to around 4 hours of direct sun during midday, so it tends to be yellow looking. With hot weather I may water every other day and I spray 3-4 times a day with r/o water.
The amount of water you should give will depend on the type of soil mix the plant is growing in. If gravelly then you are safe with watering til it pours out the bottom of the pot. If peaty sand or mix that looks like it gets mucky when wet then just dampen the surface of the soil with spraying and only water heavy weekly. The plant does not like wet feet, only dampness. Recommended soil mix is a blend of granitic gravel and leaf mold.
I cannot make any recommendations on fertilizing. I have not done any consistent experiments with fertilizing Selaginellas but would think that fish emulsion would be the safest to use and probably in half dilutions to be on the safe side.