What is the minimum magnification that one would need to discern a pair of binary stars if viewed from Earth? Are there factors other than magnification that matter? If so, why?
There are many other factors that would matter for obvious reasons, including:
Distance of the pair from Earth.
Actual brightness of the stars in the pair.
The orientation of the pair. For example, is one currently in front of the other?
The intervening medium between us and the pair, dust for example.
Distance of the stars in the pair from one another.