What does it mean by 大地を見る in Kotomi's essay?
This seems to be a somewhat obscure reference to the original Gundam anime.
Specifically the preview for Episode 5. It goes:

重力に任せて落ちれば燃え尽きてしまう大気圏突入。
その瞬間にシャアはホワイトベースに奇襲を掛けた。
我も危険なら彼も危険、共に大地を見ることができるのか？　
機動戦士ガンダム、次回「大気圏突入」。
君は生きのびることができるか！

The title of Episode 5 is literally &quot;Plunging into (the) atmosphere&quot; (officially, its &quot;Reentry to Earth&quot; ). Implying some sort of double entendre, likely implying illicit intercourse.
I can't comment much on the style of writing in particular, but overall such an abstruse wording is not uncommon in literary Japanese. The Japanese people seem to enjoy euphemizing and beating around the bush in their writings. The specific nuances are very difficult to translate.
For an example:

Natsume Soseki once taught his students that the correct Japanese translation for “I love you” is “Tsuki ga tottemo aoi naa” (The moon is so blue tonight); what he meant was that to express within the Japanese cultural framework the same emotion expressed in English by “I love you,” one must choose words like “The moon is so blue tonight.”
(from Sato Kenji’s “More Animated than Life: A Critical Overview of Japanese Animated Films,” Japan Echo, 12/97)