The first is similar to the Omnipotence Paradox and a Chinese proverb about a spear that can pierce any shield and a shield that can deflect any strike. Logic says that an unstoppable object or being cannot exist at the same time as an immovable object or being otherwise they are not what they say they are. However there are a few theories I've heard:
1) The unstoppable object bounces off the immovable object.
2) The unstoppable object stops whilst the immovable object moves.
For the second, technically Pyro can't control Sunfire's fire because Sunfire's power isn't fire - it's solar radiation and plasma. A better question would be Pyro vs the Human Torch. I think it would be a draw:
1) They can both control fire.
2) They are both immune to fire in some way.
However, Pyro is only immune to fire that's under his control so he'd have to always be on the defensive; taking control of any fire that comes near him.