Is it conceivable that the recurring problems I face in the house I live in are due to the evil eye, and would moving out of this house be sufficient to solve them, based on the rulings of the Qur'an and the Sunnah?

Indeed, the evil eye is real and not improbable; it can afflict family members without affecting the house itself. To treat the evil eye, it is recommended to learn and recite the prescribed dhikr (remembrances) with conviction, and to consistently recite the Qur’an and the daily and nightly dhikr. If the person who cast the evil eye is known, they should be commanded to perform ablution (ghusl (definition)), and the water should be poured over the afflicted person. Leaving the house is not necessary, but if a person is frequently afflicted and surrounded by envious neighbors, changing residence might be better for their comfort.