I wouldn't eat feta that's more than a few days old, unless it was kept in brine. You may use plain water or milk if you want to reduce the saltiness, but without some sort of liquid it doesn't keep more than a week - max. I don't know how that French version of yours was made, but it doesn't sound like any feta I know. Greek feta, when it goes bad, may get moldy or develop a yellowish tint on the outside. You can cut it off and eat the rest, but it may have an unpleasant smell. In that case you can't eat it raw, but you can still use it in pies, fritters, etc.
It's the same in Greece. Dolmades (or more commonly dolmadakia, meaning little dolma) are always hot and contain meat. The meatless version (dolmadakia yalantzi) is eaten as a main course during Lent, but when used as an appetiser, it is always cold.
Falafel no. Various recipes which involve frying balls of chick peas, yes. The best known are "pittaroudia", a specialty of the island of Rhodes, but there are others too. The main difference with the Arabic falafel is that in greek recipes the chickpeas are never raw and there is no tahini. Here is a quick one, using yesterday's leftovers: Mash the cooked chickpeas - sauce, spices and all. Add a generous amount of feta cheese (other crumbly white cheeses with a strong taste will do fine). Add finely chopped parsley and salt, pepper, oregano to taste. Add two eggs, well beaten, and some flour to get a thick consistency, but not so firm as to form balls. Spoon dollops of the mixture into hot oil and fry from both sides. Can be eaten hot (better) or cold. Makes a nice substitute to meat in sandwiches.