Let me address each of your points:
- Home Prices and Interest rates are in inverse proportion to each other
This is not necessarily true at all. Home prices are driven by supply and demand, not by interest rate. It might be true that when rates go up, the demand for houses goes down, as fewer people can afford a house. But in any individual location, other factors will affect prices a lot more than just interest rate changes.
- I have friends who rushed to buy houses this year because according to them it is the best time to buy a house because rates are so low(they completely disregarded the fact that home prices are so high). I dont think it is smartest of the moves. Am I right or wrong thinking that?
I don't think rushing to buy a house is ever a good idea. You should buy a house when you are ready to buy a house, and speculating on whether the housing prices or rates will go up or down is not productive.
- Extending on #2, if prices and rates are inversely proportionate then I think anyone would end up paying the same mortgage regardless of when he/she buys a property because your mortgage is affected by both.
As I said in #1, it simply isn't true that interest rates and housing prices are exactly proportional. But I will agree with you that it is short-sighted to rush to buy a house before you are ready because you think that the rates are going up, and not even consider other factors, such as housing prices. On the other hand, if you are already in a situation where you are ready to buy a house, it doesn't make sense to wait, either, especially if you think that the rates will go up.
- In short, is rate hike a good news or bad news for a home buyer?
This is just my personal opinion, but if I am buying a home, I want the interest rate to be as low as possible. I would certainly not be happy if the rate went up just before I was ready to buy. However, as borrowing rates go up, interest rates paid on savings accounts will also go up, which is good news for the saver and investor (I am both). As a result, I'm not too concerned about interest rates either way.