This is great, keep up the lucid dreaming! I'm not sure about your last question, but I can answer your first two questions.

A WILD by definition is a wake-induced lucid dream. In other words, you go from the awake state to the dream state, lucid, so you enter a lucid dream. If you have a 'WILD' in a dream, then it's technically not a WILD, but a DILD. The same applies for SP; it's only actual SP if you are in the state between awake and dream. I would argue, however, that if you have what appears to be a WILD in a dream, it doesn't matter that it isn't real. If you keep a total of how many of each type of lucid dream you've had, then I would say it should go under DILD, but the end result is the same; you still become lucid. And if you keep up your reality checks when you wake up after sleeping, having a false awakening after you become lucid shouldn't be a problem.

ShockWave.