Major Update:
It took them three weeks, but they got me a almost new engine with only 6000 miles on it. It has been driving great, I have about 200 miles on it so far. Has not lost oil. Physically also, the engine looks great. They covered it under warranty.
But wait a second....
My troubles are not over yet. Since yesterday, I am noticing that car hesitates and starts shaking after 65MPH. If I try to accelerate beyond 65MPH, I feel hesitation and the car will start shaking erratically. This has me scared to death, and also frustrated beyond your wildest imagination. Its like the problems will never end.
I have checked the transmission fluid level, its fine and the color is cherry red. The engine has not burned a drop of oil yet, and oil looks very clean.
Is it my engine or transmission? Is it possible that they did not mate the engine with transmission properly and thats why it is hesitating? But then why does it hesitate only at higher speeds. It drives totally fine under 60MPH.
Any advice greatly appreciated. Hope I don't need to change the transmission too now. Never had this hesitation problem before. Though my previous engine burned oil, I never had hesitation problem.