Q: What would be the right activity of the Buddhi when it opens or surrenders itself to the Mother?
The right activity of the buddhi is always to observe, discern, discriminate, understand rightly and give the right direction to the vital and the body. But it does it imperfectly so long as it is in the Ignorance; by opening to the Mother it begins to get the true light and direction. Afterwards it is transformed into intuition and from intuition to the instrumental action of the overmind or the supermind Consciousness.
Q: How does the Buddhi begin to open or surrender to the Mother?
By recognising its own ignorance and aspiring for light and transformation.
Q: Can it by itself have the right activity or must it be enlightened by the higher consciousness to do so?
If it is trained, it can act rightly within its limits, — but that does not give the higher Truth.
– Sri Aurobindo