Is playing Surat Al-Baqarah audibly sufficient to prevent devils from entering the house for three days, or is it a condition that it be recited from the Mushaf by one of the household members? And does reciting Surat Al-Baqarah prevent the Qarain (jinn companions) from entering the house?

Reciting Surat Al-Baqarah is a great act and expels Satan. It is not a condition to raise one's voice with it, or to recite it all at once, or for it to be recited by only one person. Listening to the Surah as a recording is not sufficient to attain its blessings, because what is required is direct recitation by the household members. As for the Qarin (companion jinn), it does not leave a person, and expelling it is achieved through continuous worship and striving. Its presence is not affected by the recitation of Surat Al-Baqarah, but its evil departs with worship.