What is the ruling on the prayer of one who keeps a dog in his house, and is it permissible to raise a dog without violating religious law?

It is not permissible to keep a dog except for hunting or guarding. The basic principle is to avoid touching dogs due to their impurity. Your prayer after purification is valid. It is advisable to abandon raising puppies and instead occupy oneself with what benefits in this world and the Hereafter.