Saying Salam upon entering a house is recommended, not obligatory, regardless of whether anyone is present.

With regard to du'a for entering the house, one should mention the name of Allah, remember Allah and give the greeting of salaam, even if there is no one in the house. For more, please see the detailed answer.

The reason for the prohibition of sleeping on one’s belly is that it was forbidden by the Prophet who said to a man who was sleeping on his belly: “Do not lie like this, for this is how the people of Hell lie.”