From the development history of Chinese characters, seal script is the earliest font (seal script includes Oracle Bone Inscriptions, bronze inscription, big seal script and small seal script). In the history of calligraphy, there are five styles of calligraphy, namely:
Seal script-including Oracle Bone Inscriptions, bronze inscription, big seal script and small seal script.
Official script-including bamboo script and silk script
True (block letters) books-including Wei Bei.
Run scripts-including running scripts.
Cursive script-including Cao Zhang, Cao Jin, cursive script and wild script.
After the Song Dynasty, due to the invention of movable type printing, a special font for printing-Songti was produced.
In modern times, due to the widespread use of book printing, other printing fonts began to appear, such as bold fonts you mentioned, and fonts that people often use, such as advertisements, comprehensive arts, amber and so on.
Therefore, there should be calligraphy fonts before printing fonts, and printing fonts are mostly evolved from calligraphy fonts.
2. The Liu Ti and inkstone styles listed above are a kind of regular script, which is formed by the calligrapher's personal style (Weibei is a font formed in the process of text evolution). The creator of Liu Style is Liu Gongquan, and the creator of Yan Style is Yan Zhenqing. They all came from the Tang Dynasty and belonged to the four masters of regular script (the other two were Ou Yangxun and Zhao Mengfu in the Yuan Dynasty).
From the analysis of the first question, we can see that in the history of writing development, seal script is followed by official script, cursive script, running script and regular script, so their appearance is related.
As for Song Style, Imitation Song Style and Bold Style, they all belong to printed fonts. Song style first appeared, followed by imitation Song style and bold style.
There are cursive fonts in the computer, but not many. I've used it before, and I forget what font it is. It's called "Yellow Grass" and it's beautiful. You can find this font on the Internet. There should be one.
4. Song style was invented by Qin Gui, which has been controversial in history because there is no official record. According to folklore, Qin Gui invented Geti, which was called Qinti at that time, but later generations hated its name and changed it to Geti, which has been used ever since. But one thing is certain: Song style must have been invented by Song people.
There is also a legend that later generations (Qin Gui) created the imitation song style when imitating Song Huizong's "thin gold body".
Seal script (Xiao Zhuan) is the standard font synthesized by Li Si in Qin Dynasty.
In Qin Shihuang's time, there was a man named Cheng Miao who studied the improvement of writing in prison. He wants to make the circle in seal script even and symmetrical, so as to write quickly and facilitate the operation of general official documents, so it is called official script.
Zhang Zhi, who spread the Han Dynasty, invented cursive script.
Between regular script and cursive script is a running script, which is fluent in writing and flexible in using a pen. It is said that it was made by Liu Desheng in the Han Dynasty.
As for boldface, it is a printing font that only appeared in modern times. I haven't seen the information of the inventor yet.
Except for Li Si's improvement of seal script, none of the above is proved by sufficient historical data, only unofficial history or his notes at that time mentioned it slightly. Some of them are even folk rumors. For reference.