Is it permissible to fast, pray, and perform qiyam in a house that has a dog, knowing that the dog's presence is against my will, and does the dog prevent angels from entering and circling around me when reciting the Quran and performing dhikr?

The presence of a dog in the house does not invalidate fasting or prayer. However, it prevents angels from entering the house and diminishes the owner's reward by two qirats every day, unless it is a hunting dog or a livestock dog. As for living with a woman, it is not permissible if it leads to khalwa (private seclusion) or seeing what is impermissible to see, based on the Prophet's (peace be upon him) saying: "No man should seclude himself with a woman, for Satan will be the third party between them."