With as far as technology has advanced, I would argue that it is possible to survive and have a good quality of life without fire or the wheel, but it's really not practical or sustainable.
Some people manage to live their lives with no fire at all. Food may be cooked on an electric stove-top, water may be heated by electricity, and there are a number of energy sources which do not requite combustion. At least when we consider fire that occurs on Earth, it is possible to live without it. If certain fires-- like the Sun-- were to cease to exist, we would certainly die. With all of that being said, the number of people on this planet who could live without fire is significantly smaller than those who rely on fire on a daily basis. Much of the world uses fire on a daily basis to cook food, heat and sterilize water, and provide warmth in the home. If fire were to cease to exist, these people might not have a secondary course of action and would certainly suffer.
I think that the wheel would be much harder to remove from our lives while maintaining the quality we're accustomed to. Wheels aren't only vital to transportation, they are a simple machine incorporated in most modern conveniences. Wheels are a part of industrialized life, so unless people are willing to adopt a mechanically simpler and far more labor intensive lifestyle, I don't think that we could get by as easily without the wheel.