I do aim if possible to write a fuller answer to this question (because I always like addressing Taiping questions as specifically as possible), but it is late where I am. So, to offer some satiation of your initial curiosity for the night, you may find these past threads cover a decent if limited chunk of your queries:

New state+government and nature thereof:

• In pre-modern China, were there ever any political movements advocating for forms of government other than dynastic monarchies? (invited follow-up to answer by /u/cthulhushrugged)

• What were the Taipings post war plans for the Qing empires territory?

• What did the rank and file of the Taiping Rebellion Believe about the cause they were fighting for?

Economic reform:

• What was the economic and social program of the Taiping Heavenly Kingdom?

• On the Wikipedia page for Taiping Heavenly Kingdom, it claims Hong Rengan wanted to build railroads in Chinas 21 provinces. Where is the number 21 coming from?

Ethnicity:

• Why were both Taiping and Qing armies so extraordinarily violent to POWs and civilians? (Manchus)

• What did the Taiping think of Judaism and Islam?