Go to any realtor website, and you will invariably find a "Mortgage Calculator" function that lets you estimate your total monthly payments. They're not selling the home to you based on the price. The reality is that they're selling the home to you based on how much you can afford to pay on a monthly basis.
No. It means I can afford to buy an already higher priced home, not your home you just increased the price for thinking (stupidly) I would pay more than you wanted last month just because now I can afford to pay more.
Lower interest rates generally mean people are willing to buy more of a home than they considered before, not the same home they considered before but now for more money.