If they are apparently observing Islam that is based on the two testimonies of faith, then they are regarded as Muslims even if they believe in some misguided ideas.
It is permissible to buy and sell hunting dogs. It is not permissible to purchase other kinds of dogs. However, one can pay money in exchange of the owner letting go of his right over the dog.
There is punishment mentioned in the Holy Quran with regards to the homosexuality. However, it is mentioned in the Sunnah – narrations of the prophet and the imams of the Ahlulbait.
Magic is prohibited. Yes, if one is required to stop the effect of magic by using magic itself, and being under the effect of magic is harmful, then it is permissible to terminate magic by magic.
