Did any era's Samurai know Outdoors Survival Knowledge? If so, which eras, which country (or however Japan separated its land at that time), and how much did they know?
As a rule, no. Samurai, by definition, were servants of their lord. The word samurai means to attend or to serve. If you are "surviving", meaning living off by yourself in the woods somewhere, you are not attending your lord are you? Feeding and supporting samurai was a huge expense for lords and it was expected by the samurai that they would be fed and equipped by their lord. Samurai were not taught subsistence survival skills, nor did they cultivate such skills because that would mean being apart from their Lord and other samurai--a dishonorable thing.
Even apart from samurai, Japan is a group culture and people, samurai or commoners alike, are expected to be a part of the group and act communally, not go off and support themselves alone in the wilderness.
Even when a samurai was cast out and became a ronin (a very bad thing), he still acted in communal manner. For example, I saw one account of a ronin who after he was cast out he made a living by making bird cages from reeds and selling them.
Another factor to keep in mind is that "hunting" in Japan is not regarded the same way as it is in the United States. In Japan every square inch of land belongs to someone and you cannot just go around killing animals or fishing in random places like you can in America. To do so without the permission of the lord or priest or whomever that owns the place would be illegal.