is it known how each kanji/compound graphic design evolved the way they did?

Question

In many languages you can know the etimology of the words, you can trace how its meaning evolved and their origins, the meaning of the words usually comes from other words in Latin, Greek, English, etc, slightly modified. Is there something like that in japanese but not for the meaning of the words, but for the graphic design of each japanese kanji/compound? For example, it is clear and it makes sense than the kanji for "forest" is made up of 3 "trees" components, or than the kanji for hermit is the addition of the "person" plus the "mountain" kanjis. Can you visually trace any component of a kanji/compound like that?

Answer 1

日本語

質問の趣旨は日本語になっている漢字の表意文字（あるいは象形文字 pictogram）についての事例紹介だと思われる。 漢字は日本で発明されたものでないので、各文字の現代における形については例えばここで調べると良い。なお、ＯＰが求めている象形文字に関しては、同じ文献のPictogramsという章で少し説明されている。なお、漢字をまねして日本で独自に作った象形文字として、和製漢字 kokujiがある。この文献の英語版はないが、ドイツ語版、フランス語版、スペイン語版があるので言葉が分かれば読むと良い。

なお、漢和辞典を見ると、一般に見出し漢字ごとに、「語源 etymology」のところに、その漢字の形に関する説明があるので、ＯＰの質問の回答として利用できると思う。

以下に参照すべきいくつかの文献等を紹介する

- 漢字/漢和/語源辞典, where you can see the origin of [every]{LLLLL} Kanji

• Chinese character classificationという文献のpictogram
• Chinese pictogram
• Video: 36 CHINESE PICTOGRAM CHARACTERS

English

I understand that the OP's question is about the etymology of kanji or Chinese character. And more, it is about the etymology not about the meaning of them but the graphic design of them, and is also asking for further examples other than 森 or 仙.
According to this article here, kanji's creation is classified in six categories, and their brief explanations are from here.

• 象形文字 Pictograms (4% of characters)
  Characters in this class derive from pictures of the objects they denote. Examples include 日 for "sun", 月 for "moon", 木 for "tree" or "wood", 山 for "mountain", and 象 for "elephant".　
• 指事文字 Simple ideograms
  Also called simple indicatives, this small category contains characters that are direct iconic illustrations. Examples include 上 "up" and 下 "down", originally a dot above and below a line.
• 会意文字 Compound ideograms (13% of characters)
  Also translated as logical aggregates or associative compounds, these characters have been interpreted as combining two or more pictographic or ideographic characters to suggest a third meaning. Commonly cited examples include 休 "rest" (composed of the pictograms 人 "person" and 木 "tree") and 好 "good" (composed of 女 "woman" and 子 "child").
  As for 森 shown by OP is categorized in this class. 森 "forest" is composed of three trees, which means 森 having many trees. 仙 is also categorized in this class.
• 形声文字 Phono-semantic compounds
  Semantic-phonetic compounds or pictophonetic compounds are by far the most numerous characters. These characters are composed of two parts: one of a limited set of characters (the semantic indicator, often graphically simplified) which suggests the general meaning of the compound character, and another character (the phonetic indicator) whose pronunciation suggests the pronunciation of the compound character. In most cases the semantic indicator is also the radical under which the character is listed in dictionaries.
  Examples are 河 "river", 湖 "lake", 流 "stream", 沖 "surge", 滑 "slippery". All these characters have on the left a radical of three short strokes (氵), which is a reduced form of the character 水 meaning "water", indicating that the character has a semantic connection with water. The right-hand side in each case is a phonetic indicator. For example, in the case of 沖 "surge", the phonetic indicator is 中, which by itself means "middle". In this case it can be seen that the pronunciation of the character is slightly different from that of its phonetic indicator; the effect of historical sound change means that the composition of such characters can sometimes seem arbitrary today.
  Xu Shen (c. 100 AD) placed approximately 82% of characters into this category, while in the Kangxi Dictionary (1716 AD) the number is closer to 90%, due to the extremely productive use of this technique to extend the Chinese vocabulary.
  This method is still sometimes used to form new characters.
• 会意兼形声文字 Compound ideograms and also Phono-semantic compounds
  Examles: 友 for "friend", 円 for "circle", and 切 for "cut", which are from here.
• 国字 Kokukji or Kanji made in Japan
  Examles: 凧 for "kite", 働 for "work", and 鰯 for "sardine", which are from here.

Last but not least, 漢字/漢和/語源辞典 might be very useful to fulfill your request, where you can get the class of every kanji, though it is written only in Japanese.