这是你想要的效果吗?

\documentclass[12pt]{ctexart}
\usepackage[most]{tcolorbox}

\usepackage{lipsum}
\usepackage{hyperref}

\usepackage{pifont}


\newcounter{question}[section]
\newcounter{answer}[section]

\NewTColorBox{question}{}
{enhanced, fonttitle=\bfseries, title={\refstepcounter{question}\label{que:\thesection-\thequestion}Question~\thesection-\thequestion\hfill \ding{43}~\pageref{ans:\thesection-\thequestion}}}

\NewTColorBox{answer}{}
{enhanced, fonttitle=\bfseries, title={\refstepcounter{answer}\label{ans:\thesection-\theanswer}Answer~\thesection-\theanswer\hfill \ding{49}~\pageref{que:\thesection-\theanswer}}}

\begin{document}
\section{这是第一章节}
\begin{question}
    \[
        a^2 + b^2 = c^2
    \]
\end{question}
\lipsum[1-10]


\begin{answer}
    \[
        a^2 + b^2 = c^2
    \]
\end{answer}

\end{document}

1.

\hbox_set:Nn \l_indent_box {\noindent 这是缩进}

中的 \noindent 是不必要的.
2.

\NewDocumentEnvironment{hindent}{+m}

你需要 m 型参数, 但是你下面环境却没有给参数, 我猜测你想要的是 +b.
3.

\coffin_join:NnnNnnnn \l_indent_coffin {t} {r} \l_text_coffin{t}{l}

需要 8 个参数, 但是你只给了 6 个.

你可以使用行内盒子

\documentclass[10pt]{article}
\usepackage{tcolorbox}
\usepackage{lipsum}
\newtcbox{\mybox}{colback=red!5!white,
colframe=red!75!black}
\begin{document}
\lipsum[1]

\mybox{This is my own box.}

\lipsum[1]

\end{document}

你可以使用 \mathop

\[
  \mathop{\arg\max}\limits_{x \in S}
\]

你也可以使用 `

你的 MWE 在我电脑上是正常的，我的环境为 texlive2023 + xelatex.

可以使用 graphbox 包提供的 align = t 选项.

此外, 使用 \parbox 或者 minipage 的 t 选项时, 建议在最顶部加上一个 \null.

\noindent\parbox[t][0.3\textwidth][t]{\textwidth}{
    \parbox[t][0.3\textwidth][t]{0.3\textwidth}
    {\null\includegraphics[width=0.3\textwidth, align = t]{example-image-1x1.pdf}}
    \parbox[t]{0.65\textwidth}{\null\Large
        456\\789
    }
}

完整代码:

\documentclass[draft,
a4paper,zihao=-4,
twoside,openany]{ctexart}
\usepackage{graphicx}
\usepackage{mwe}

\usepackage{graphbox}
\usepackage{calc}
\begin{document}


\noindent\parbox[t][0.3\textwidth][t]{\textwidth}{
    \parbox[t][0.3\textwidth][t]{0.3\textwidth}
    {\null\includegraphics[width=0.3\textwidth, align = t]{example-image-1x1.pdf}}
    \parbox[t]{0.65\textwidth}{\null\Large
        456\\789
    }
}

\end{document}

没什么大问题，少了个 at.

% \node [fill=red,inner sep=1pt,label={below:$H$},circle] (H) {};
\node [fill=red,inner sep=1pt,label={below:$H$},circle] at (H) {};

使用一个宏包之前请认真阅读一下宏包手册.

tkzelements 环境内是 lua 代码, 所以注释符应该使用 lua 的注释符 --.

实际上在宏包手册中也有很多注释, 只是你从来没有认真看过.

试试 \string

\newwrite\out
\immediate\openout\out=out.tex
\immediate\write\out{%
  \string\pageref{myref:\mynum}
}
\immediate\closeout\out

得到

\pageref{myref:1} 

\newlength{\leftmarkwidth}
\renewcommand{\headrule}{%
    \settowidth{\leftmarkwidth}{\leftmark}%
    \vspace*{-.5\baselineskip}%
    \vrule width \leftmarkwidth height .5pt\relax%
}

\documentclass[12pt]{ctexart}
\usepackage{amsmath}
\usepackage{fancyhdr}
\usepackage{lastpage}
\usepackage{lipsum}
\pagestyle{fancy}
\fancyhf{}
\renewcommand{\thepage}{\roman{page}}
\newlength{\leftmarkwidth}
\renewcommand{\headrule}{%
    \settowidth{\leftmarkwidth}{\leftmark}%
    \vspace*{-.5\baselineskip}%
    \vrule width \leftmarkwidth height .5pt\relax%
}
\fancyhead[L]{\leftmark}
\fancyfoot[C]{第 \thepage 页,共 \pageref{LastPage} 页}
\begin{document}
\section{如何入门\LaTeX{}}
\lipsum[2-6]
\section{如何进一步学习\LaTeX{}Long Long Long Long Long Long}
\lipsum[2-6]
\section{如何系统性学习\LaTeX{}}
\lipsum[2-6]
\section{如何入坑\LaTeX{}}
\lipsum[2-6]
\section{如何放弃\LaTeX{}Long Long Long Long}
\lipsum[2-6]
\end{document}

ctexart 修改了默认行距, 所以才会出现这个问题，可以尝试修改行距

\documentclass[12pt]{ctexart}
\usepackage{amsmath}
\usepackage{longdivision}
\linespread{1}\selectfont
\begin{document}
\[
    \longdivision{1024}{8}
    \quad
    \longdivision[4]{114514}{233}
    \quad
    \longdivision[2]{666.666}{88}
    \quad
    \longdivision[repeating decimal style = dots ]{5.3}{37}
\]
\end{document}

注意报错信息 You must invoke LaTeX with the -shell-escape flag.

因为 minted 包是借助 python 的 pygments 库完成代码高亮渲染的, 需要和外部程序完成交互，所以需要开启 -shell-escape 编译参数.

鉴于你使用的 texstudio 编辑器, 可以参考下图配置编辑器以开启 -shell-escape.

上图来源于某 qq 群，图中以 lualatex 为例，如果您习惯使用 xelatex 或者 pdflatex, 请修改对应的编译参数即可.

只需以 description 节点为基点做平移即可

\documentclass{book}

\usepackage[explicit]{titlesec}

\usepackage[margin = 2cm]{geometry}
\usepackage{enumitem}
\usepackage{tikz}


\usepackage{graphbox} % provide align = c 

\makeatletter
\def\@chapter@description{}
\def\@chapter@objectives{}
\titleformat{name = \chapter}{}{}{0em}
{%
  \begin{tikzpicture}[remember picture, overlay, every node/.style={inner sep = 0pt, outer sep = 0pt}]
    \node[anchor = north west] at ([shift = {(2cm, -2cm)}]current page.north west) {\includegraphics[width = .2\textwidth, height = \textheight]{example-image}};
    \fill[gray!40] ([shift = {(2cm + .2\textwidth, -2.5cm)}]current page.north west) rectangle ++ (.8\textwidth, -4cm);
    \node[anchor = south west, inner sep = 10pt, scale = 2, font = \bfseries] at ([shift = {(2cm + .2\textwidth, -6.5cm)}]current page.north west) {#1};
    \fill[gray!70] ([shift = {(-2, -2.5)}]current page.north east) rectangle ++ (-1.5, -4);
    \node[rotate = 90, font=\bfseries\Large]  at ([shift = {(-2.75, -4.5)}]current page.north east) {\chaptername\ \thechapter};
    \node[anchor = north west, inner sep = 10pt] (description) at ([shift = {(2cm + .2\textwidth, -6.5cm)}]current page.north west) {
      \begin{minipage}{\dimexpr .8\textwidth - 10pt\relax}
        \parindent=2em
        \@chapter@description
      \end{minipage}
    };
    \fill[shading=radial, left color=startcolor, right color=stopcolor] ([shift = {(1, -.5cm)}]description.south west) rectangle ++ (.7\textwidth, -0.8cm);
    \node[anchor = west, inner sep = 10pt, scale = 1, font = \bfseries] at ([shift = {(1, -.9cm)}]description.south west) {Objectives};
    \node[anchor = north west, inner sep = 10pt] at ([shift = {(1, -1.9cm)}]description.south west) {
      \begin{minipage}{\dimexpr .8\textwidth - 10pt\relax}
        \parindent=2em
        \@chapter@objectives
      \end{minipage}
    };
  \end{tikzpicture}
}
\newcommand{\icon}[1]{\includegraphics[height=1em, align = c]{#1}}
\NewDocumentEnvironment{fancychapter}{m+m+b}{%
  \def\@chapter@objectives{#3}
  \def\@chapter@description{#2}
  \chapter{#1}
  \newpage
}{}
\makeatother

\usetikzlibrary{calc, intersections}
\begin{document}
\setlist[itemize]{noitemsep, leftmargin=*, label=}
% 定义渐变色
\definecolor{startcolor}{RGB}{128,128,128} % 起始颜色为黑色
\definecolor{stopcolor}{RGB}{245,245,245} % 结束颜色为白色
\begin{fancychapter}{Introduction \LaTeX}{
    The principles of object-oriented programming, such asmodularity and reusability, are quite popular as they helpin reducing the complexity of programs. In order toimplement such principles in real world applications, suchas library management and nventory management, youneed to make use of an object-oriented language, such asJava.

    This chapter focuses on the fundamentals and buildingblocks of the Java programming language. In addition, itexplains how to access the class members.

    The principles of object-oriented programming, such asmodularity and reusability, are quite popular as they helpin reducing the complexity of programs. In order toimplement such principles in real world applications, suchas library management and nventory management, youneed to make use of an object-oriented language, such asJava.

    This chapter focuses on the fundamentals and buildingblocks of the Java programming language. In addition, itexplains how to access the class members.
    
    The principles of object-oriented programming, such asmodularity and reusability, are quite popular as they helpin reducing the complexity of programs. In order toimplement such principles in real world applications, suchas library management and nventory management, youneed to make use of an object-oriented language, such asJava.

    This chapter focuses on the fundamentals and buildingblocks of the Java programming language. In addition, itexplains how to access the class members.
}
{
  \begin{itemize}
  \item \icon{example-image} Some test text.
  \item \icon{example-image} Some test text.
  \item \icon{example-image} Some test text.
  \item\icon{example-image}  Some test text.
\end{itemize}
}
\end{fancychapter}



\end{document}

贴一下代码，看不懂的下面评论吧

\documentclass{book}

\usepackage[explicit]{titlesec}

\usepackage[margin = 2cm]{geometry}

\usepackage{tikz}

\makeatletter
\def\@chapter@description{}
\titleformat{name = \chapter}{}{}{0em}
{%
  \begin{tikzpicture}[remember picture, overlay, every node/.style={inner sep = 0pt, outer sep = 0pt}]
    \node[anchor = north west] at ([shift = {(2cm, -2cm)}]current page.north west) {\includegraphics[width = .2\textwidth, height = \textheight]{example-image-a}};
    \fill[gray!40] ([shift = {(2cm + .2\textwidth, -2.5cm)}]current page.north west) rectangle ++ (.8\textwidth, -4cm);
    \node[anchor = south west, inner sep = 10pt, scale = 2, font = \bfseries] at ([shift = {(2cm + .2\textwidth, -6.5cm)}]current page.north west) {#1};
    \fill[gray!70] ([shift = {(-2, -2.5)}]current page.north east) rectangle ++ (-1.5, -4);
    \node[rotate = 90, font=\bfseries\Large] at ([shift = {(-2.75, -4.5)}]current page.north east) {\chaptername\ \thechapter};
    \node[anchor = north west, inner sep = 10pt] at ([shift = {(2cm + .2\textwidth, -6.5cm)}]current page.north west) {
      \begin{minipage}{\dimexpr .8\textwidth - 10pt\relax}
        \parindent=2em
        \@chapter@description
      \end{minipage}
    };
  \end{tikzpicture}
}

\NewDocumentEnvironment{fancychapter}{m+b}{%
  \def\@chapter@description{#2}
  \chapter{#1}
  \newpage
}{}
\makeatother
\begin{document}


\begin{fancychapter}{Introduction \LaTeX}
  \foreach \x in {1, ..., 100} {Some test text. }
  
  \begin{itemize}
    \item Some test text.
    \item Some test text.
    \item Some test text.
    \item Some test text.
  \end{itemize}
\end{fancychapter}

\end{document}

你能提供一个 mwe 吗