2. No, blightburn is a sickness/disease/radiation, not a poison.
In Pathfinder radiations are treated as a form of poison.It is a fun fact that Druids that are 9th level and above are immune to radiation damage, something that is really counterintuitive.
RadiationRadiation is a very real threat to those who explore the technological ruins of Numeria. Radiation is a poison effect whose initial effect causes Constitution drain and secondary effect causes Strength damage. Radiation dangers are organized into four categories: low, medium, high, and severe.
A virulent weapon magically intensifies any poison it delivers.
Any creature coming into physical contact with a blightburn crystal takes 2d6 points of fire damage per round, and creatures within 60 feet of blightburn crystals are exposed to blightburn radiation.
The radiation con damage is a AoE, not an effect delivered by the weapon, so it is not affected by the Virulent property.
1. from what I can tell, weapons cannot be made of Blightburn
AFAIK there are no stats for Blightburn, so we don't know its hardness and hit point. The other two radioactive minerals described in Heroes of the Darklands say what military uses they can have, so I agree that Blightburn probably isn't meant to be used to make weapons.
With enough magic and GM permission, anything is possible.