Reference the existing literature, and use the existing ideas to effect.

Kim Stanley Robinson's Mars Trilogy discussed balancing the gravitation and light pressure of an orbiting solar interceptor - in this case a "Soletta" used to focus solar energy into a giant heat beam for construction purposes.

This answers your question as to stability of a solar interceptor (at least at the conceptual level, if not in actual practical terms)

Larry Niven's "Mote in God's eye" discussed the consequences of the power of being able to move asteroids, and use them as weapons against planetary surface dwellers.

This may explain why nobody is yet suggesting moving an Asteroid into an Earth-captured orbit. (Other than it being almost impossible to envisage with our current technology. Moving Ceres with our existing technology, or even that planned for the next several decades would be like a single ant moving an entire mountain)