The domestic dog is a member of the genus Canis (canines), which forms part of the wolf-like canids, and is the most widely abundant terrestrial carnivore. The dog was the first species to be domesticated and has been selectively bred over millennia for various behaviors, sensory capabilities, and physical attributes.
Dog is Najis whether it is used in hunting or guarding or otherwise.
Islam does not say that it is not allowed to have a dog as a pet, but it clearly says that dog is Najis and you must avoid any Najis item, otherwise your Prayers might be invalid if your cloth or body is Najis.
Hunting and guarding dogs are out of home usually, so there is no risk of Najasah on you from such dogs, but when the dog is at home as a pet , the risk is there.
Yes, but it is better if it can stay outside (such as in a dog house, if that is possible on your property; these days, they do have outdoor heaters for animals if that is a possibility).
I am sure you are familiar with the hadith saying that having a dog inside affects acceptance of prayers; Allah knows best. Of course, we are also supposed to be compassionate, and it is not compassionate to let it freeze to death!
Yes you can interact with it and train it.
Yes, be sure to observe taharah for salat and any other necessary things such as dishes.
People have had dogs as work animals for centuries, and even the Ashab al-Kahf had a dog around them. As someone once said, it is not the dog's fault that it is najis!
It has been reported in several Islamic sources that the Prophet have said angels do not enter a house in which there is a dog or paintings and sculptures of living beings (humans and animals). These words seems to indicate that keeping a dog in the house is discouraged in Islam but not a prohibition. It has also been reported that there is no problem in having hunting and shepherd dogs. What can be concluded is therefore the permissibility of keeping dogs in gardens or outside home although it is disliked to keep them in the house. Obviously, if the presence of a dog in the house would cause excessive hardships related to hygienic issues or matters of ritual purity, keeping them in the house would become impermissible.
With prayers for your success.
Yes, there is no problem in praying there. Everything is pure until proven otherwise, in this case, you have to have seen the impurities of the dog being transferred to you, your clothes you’re praying in or the place you’re praying.