Yes, traditional Christianity generally recognizes only angels, demons, and God, though some sects don’t even recognize angels.
In some ceremonial magick systems, elementals are considered to be either a type of angel themselves or under the aegis of them. However, to my knowledge, there is nothing that says you can’t work with them if you also work with demons.
Undines are considered to be supernaturally beautiful and it is not that the undines themselves are overly lustful but that their beauty can captivate, beguile and bewitch the magician. In other words, if the magician can’t keep it in their pants, then, according to patriarchal religion, it’s the fault of the spirit, not the failure of the magician.
Undines are similar to the nymphs of Greek mythology in that they are carefree and enjoy life, which makes them, in the eyes of strict religion, “lustful.”
No, religion is. Do not confuse one for the other. They are not the same thing.
Enjoying life is not a crime. God wants you to have fun. Religion, however, does not because that makes you harder to control. For a thousand years, dance was used to celebrate God and to give thanks for being alive, for example, yet it was branded as sinful by the Church so nowadays communing with God mostly involves sitting on uncomfortable pews listening to some out of touch priest drone on about how everybody’s a sinner.
Does it say specifically that such desires are bad, or is the book simply posing the questions to make the reader think about what their magical intentions are? Remember, in magick, your intention matters and in high magick one is supposed to be pursuing the Great Work, also called one’s True Will, not material things.