1. Farm raised and even free-range and organically raised ducks and geese are indeed available in Israel but one will find them only directly from the farmers that raise them, that largely in the Galilee and on the Golan, most of them making their way to the country's better restaurants and would you believe, the "Jewish" restaurants (that is to say those restaurants seving up the dishes of Central and Eastern Europe). They are also sometimes available at the better butcher shops of the Galilee but one has to place orders in advance.
2. Israeli turkeys, in my opinion, have precious little in common with those magnificent birds of North America. In my opinion, the turkeys raised in Israel have little charm while alive and even less when placed in our ovens, their flavor and texture being watery at best. Best bet for turkey within Israel is to hold until Thanksgiving which, although not celebrated by many here, brings an influx of quite good frozen whole turkeys from the USA. Personally, I always wait until that time of the year to stock up and place 3 - 4 birds in my freezer.
3. As to wild game - the country boasts some magnificent samples of wild boar, deer, game birds (partridges, pheasants, quails) and fish - especially of course sea fish and of fresh-water fish, catfish, trout and bass that have escaped from the ponds and made their way to the Jordan river in which they today thrive. With regard to true game, the problem is that although some people are licensed to hunt, no-one is allowed to sell that meat - neither in restaurants nor privately. There are some ways around this of course and a few restaurants in the Galilee are more than happy to charge you a goodly sum for their salads and give you their meat free of charge. Alas, even that loophole is closing. High quality game is, however, available to those who have contacts in Jericho.
By the way, hunting in Israel is a very controlled operation, one of the very few areas in which the country excels in guarding its wildlife and environment! That there is a certain amount of illegal hunting is evident, but under no circumstances do I advise buying from sources, that for both moral and health reasons.