- I understand this phrase to mean “how the mind is disposed” and “how the mind is reacting (to its object)”. The word at issue is nimitta, which can also carry a meaning of “cause or condition”. For example, the word samādhinimitta occurs a lot in the suttas, which could be understood as “cause for samādhi” – in other words, what the mind does or the object it takes up that causes samādhi to arise.
In practical terms, I take this to mean that one needs to be sensitive, adaptable, and responsive during practice, noticing the mind’s state and becoming skilled in creating the conditions for it to become collected and unified.
- I think Venerable Anālayo could answer this question best. This is from Perspectives on Satipaṭṭhāna:
The Saṃyutta-nikāya parallel indicates that the foolish cook fails to notice whether the king or minister he is serving took much of something, or whether he reached for a particular dish and praised it. In both versions the example of the foolish cook illustrates a form of practice of the four satipaṭṭhānas that is not successful in overcoming defilements and in settling the mind so as to lead it into concentration.
Applying this simile to mindfulness of breathing, the breath as such is a bland object, devoid of intrinsic interest. Some meditators may be naturally capable of successfully directing their mind to this object and sustaining it there, but others find this difficult, simply because the breath as such does not attract one’s attention. Their predicament could be compared to being given a plate of plain rice, which on its own is tasteless. Just as with only plain rice, one would soon be on the lookout for something to add flavour to the meal, so the mind directed to an insipid object like the breath can find it boring and naturally turns to something tastier, like reviving memories of the past or devising plans for the future. When this happens, one need not stoically continue to swallow down plain rice, perhaps even counting each morsel of rice eaten as an additional measure to enforce the meal. Instead, with the help of the sixteen-steps scheme, one can take an alternative approach that keeps the mind more easily engaged with its object.
In order to please the mind, the skilful cook can accompany the plain rice with sixteen different dishes, according to the recipe given in the Ānāpānasati-sutta and its parallels. This would ensure that the breath becomes tasty enough for the mind to be pleased and remain interested. Appetizing the breath in this manner, by introducing a variety of perspectives and encouraging the arising of wholesome types of pleasure and joy, will go a long way in helping the mind to stay with the breath. The reason is that this approach naturally arouses interest in the object chosen for meditation practice.
As with the awakening factors, mindfulness and joy are important “kitchen appliances”. Mindfulness not only attends to the breath, but is also aware of various aspects related to the breath. Most importantly, mindfulness is aware of how the mind is taking to the present practice, just as the skilful cook needs to be aware of what dish the master prefers. With established mindfulness one realizes what pleases the mind, what arouses wholesome types of joy, and what makes the mind become interested and engaged. This can then be used skilfully to promote progress in the practice. Needless to say, the same applies to practice of the four satipaṭṭhānas that is not based on the breath. Skilfully working in line with the natural tendencies of the mind in this way can go a long way in speeding up one’s progress on the path.
You might find it helpful to emphasize gladness and joy (from wholesome sources) earlier in the meditation, perhaps by appreciating the subtle joy of the present moment or by enjoying the tranquility of the body and breath. The brahmavihāras can also be aroused in order to soften the mind and gladden it, perhaps as an “appetizer” before beginning the ānāpānasati practice. Other common EBT methods for arousing gladness are reflecting on the Buddha, the Dhamma, the Sangha, your own generosity, your own sīla, or the qualities you share with the devas. If none of these are helpful, you can be a creative cook and find your own way of pleasing the king. 
Once the mind is sufficiently stable and there is gladness, joy, and pleasure, the only ingredient left would be letting go more fully into the experience, relinquishing control.
Best wishes for your practice.