Finally I found a solution to all my problems with the iPhone…After contacting the Apple iPhone technical support team over the phone (1-800-My-iPhone), they found that it could be an issue with the hardware and asked me to stop by to the nearby apple store. Before doing that they actually asked me to restore the phone and iTunes wiped everything and it failed to restore back to the old state. Even though the iTunes recognised the device; but it is not letting to perform any sync or restore operation. The local store guys with some basic questions, replaced with a new one (not really sure brand new or refurbished, but at least it does not have any refurbished marks).
Now no crashes when I connect the device to the PC nor it skips the tracks while playing the songs. Good to go and lets wait and see what happens in the coming days ! It will be really great if it can work till the 3G one is released.