the 'it' in this paragraph may refer to the gastric fire, life-force or even the kundalini. Vasistha is surely not terribly keen on making and sustaining such distinctions!
it is the yogi's theory that nectar flows from the palate, which is consumed by the gastric fire in the solar plexus - thus the cool moon is the cause of the burning fire - and he prescribes the viparitakarani to prevent this loss of nectar.
there seems to be some confusion in the last para above. However, it is clarified in chapter 126 of this section.
of course, vicara means 'direct observation or looking into'.
for the words 'thinking' and 'non-thinking' in the last paragraph above, the text uses the words 'samvedanam' and 'asamvedanam', which imply much more than mere thinking. Cognition, comprehension, feeling, experience, and knowledge, are also implied by 'samvedanam'.
cidakasa is said to be the 'void of consciousness', because it is devoid of the ego-sense.
these two verses also resemble the Gita, but with the significant alteration in the second, which makes it seem that when the student is ready, enlightenment happens.