issue with hhline and cellcolor in table

I have two MWEs: the last one cure both problems, the first does not cure the small green spaces.

Using hhline

You have forgotten to turn on arrayrowcolor{black} two places. In addition, the hhline- syntax was wrong one place. I have not found a solution for the small spaces in the horizontal borders (yet). It is the green coloured arrayrule under the multirow that overwrite the vertical line.

Not related: You load multirow twice.

\documentclass{article}
% General document formatting
\usepackage[margin=0.7in]{geometry}
\usepackage[parfill]{parskip}
\usepackage[utf8]{inputenc}
\usepackage{multirow, hhline}

% Related to math
\usepackage{amsmath,amssymb,amsfonts,amsthm}
\usepackage[table,xcdraw]{xcolor}

\renewcommand{\arraystretch}{1.2}
\setlength{\extrarowheight}{1pt}

\begin{document}    
    \begin{table}[!ht]  
        \centering
        \begin{tabular}{|c|c|c|}
            \hhline{-~~}
            {\cellcolor[HTML]{C0E5C6}}Modell-Überkategorien   &\multicolumn{2}{c}{}    \\ 
            \hhline{-~~}
            statisch                &\multicolumn{2}{c}{}   \\ 
            \hhline{-~~}
            zufällig (Monte-Carlo)  &\multicolumn{2}{c}{}   \\ 
            \hhline{*{3}{-}}            
            \cellcolor[HTML]{E2EFD9} & \cellcolor[HTML]{E2EFD9} Kontinuirlich & \cellcolor[HTML]{E2EFD9} \\
            \hhline{>{\arrayrulecolor[HTML]{E2EFD9}}->{\arrayrulecolor{black}}->{\arrayrulecolor[HTML]{E2EFD9}}-}\arrayrulecolor{black}
            \cellcolor[HTML]{E2EFD9} & \cellcolor[HTML]{E2EFD9} Hybrid & \cellcolor[HTML]{E2EFD9}\\
            \hhline{>{\arrayrulecolor[HTML]{E2EFD9}}->{\arrayrulecolor{black}}->{\arrayrulecolor[HTML]
{E2EFD9}}-}\arrayrulecolor{black}
\multirow{-3}{*}{{\cellcolor[HTML]{E2EFD9}}dynamisch} 
            & \cellcolor[HTML]{E2EFD9} Diskret & \cellcolor[HTML]{E2EFD9} \multirow{-3}{*}{Raum/Zeit}  \\ 
            \hhline{|---}
            \cellcolor[HTML]{E2EFD9} (Multi)-Agenten basiert &\multicolumn{2}{c}{} \\ 
            \hhline{|-~~}
        \end{tabular}
        \bigskip
    \end{table}
\end{document}

Using cals

Your tabular is much easier to build using cals.

\documentclass{article}
% General document formatting
\usepackage[margin=0.7in]{geometry}
\usepackage[parfill]{parskip}
\usepackage[utf8]{inputenc}
\usepackage{cals}

% Related to math
\usepackage{amsmath,amssymb,amsfonts,amsthm}
\usepackage[table,xcdraw]{xcolor}

\let\nc=\nullcell                                                  % Shortcuts
\let\sc=\spancontent

\definecolor{darkGreen}{HTML}{C0E5C6}
\definecolor{lightGreen}{HTML}{E2EFD9}


\begin{document}

\begin{calstable}

% Defining 3 column relativ to each other and relativ to the margins
\colwidths{{\dimexpr(\columnwidth/16*4)\relax}
            {\dimexpr(\columnwidth/16*3)\relax}
            {\dimexpr(\columnwidth/16*3)\relax}
            }
% The tabular fills 5/8 of the text area

% Set up the tabular
\makeatletter
\def\cals@framers@width{0.4pt}   % Outside frame horizontal rules
\def\cals@framecs@width{0.4pt}   % Outside frame horizontal rules, reduce
                                 % thickness if you find them too heavy
\cals@setpadding{Ag}
\cals@setcellprevdepth{Al}
\def\cals@cs@width{0.4pt}        % Inside rules, reduce if the rule is too heavy
\def\cals@rs@width{0.4pt}
\def\cals@bgcolor{}              % Define cals@bgcolor to empty

\def\green{\ifx\cals@bgcolor\empty      % Colour switch (on-off)
    \def\cals@bgcolor{darkGreen}
\else \def\cals@bgcolor{} \fi}

\def\lgreen{\ifx\cals@bgcolor\empty     % Colour switch (on-off)
    \def\cals@bgcolor{lightGreen}
\else \def\cals@bgcolor{} \fi}

\def\tb{\ifx\cals@borderT\relax     % Top border switch (off-on)
    \def\cals@borderT{0pt}
\else \let\cals@borderT\relax\fi}

\def\bb{\ifx\cals@borderB\relax     % Botton border switch (off-on)
    \def\cals@borderB{0pt}
\else \let\cals@borderB\relax\fi}

\def\rb{\ifx\cals@borderR\relax     % Right border switch (off-on)
    \def\cals@borderR{0pt}
\else \let\cals@borderR\relax\fi}

% R1 Body
\brow
    \green\alignC\cell{Modell-Überkategorien}\green
    \tb\rb\nc{lt}
    \nc{rt}\tb\rb
\erow
% R2 Body
\brow
    \cell{statisch}
    \rb\nc{l}
    \nc{r}\rb
\erow
% R3 Body
\brow
    \cell{zufällig (Monte-Carlo)}
    \rb\nc{lb}
    \nc{rb}\sc{}\rb
\erow
% R4 Body
\brow
    \lgreen\nc{lrt}
    \cell{Kontinuirlich}
    \nc{lrt}
\erow
% R5 Body
\brow
    \nc{lr}
    \cell{Hybrid}
    \nc{lr}
\erow
% R6 Body
\brow
    \nc{lrb}\sc{\vfil dynamisch}
    \cell{Diskret}
    \nc{lrb}\sc{\vfil Raum/Zeit}
\erow
% R7 Body
\brow
    \cell{(Multi)-Agenten basiert}\lgreen
    \rb\bb\nc{ltb}
    \nc{rtb}\sc{}\bb\rb
\erow
\makeatletter
\end{calstable}\par % \par needed to align the tabular

\end{document}

Small modification of first example (+1) regarding use of colors in table in the nice Sveinung answer (for exercise)):

\documentclass{article}
% General document formatting
\usepackage[margin=0.7in]{geometry}
\usepackage[parfill]{parskip}
\usepackage[utf8]{inputenc}
\usepackage{multirow, hhline}

% Related to math
\usepackage{amsmath,amssymb,amsfonts,amsthm}
\usepackage[table,xcdraw]{xcolor}
\definecolor{col1}{HTML}{C0E5C6}    % <---
\definecolor{col2}{HTML}{E2EFD9}    % <---

\renewcommand{\arraystretch}{1.2}
\setlength{\extrarowheight}{1pt}

\begin{document}
    \begin{table}[!ht]
    \centering
\begin{tabular}{|c|c|c|}
    \hhline{-~~}
\cellcolor{col1}{Modell-Überkategorien} % <---
                        &   \multicolumn{2}{c}{}    \\
    \hhline{-~~}
statisch                &   \multicolumn{2}{c}{}    \\
    \hhline{-~~}
zufällig (Monte-Carlo)  &   \multicolumn{2}{c}{}    \\
    \hhline{*{3}{-}}
\rowcolor{col2} 
                        & Kontinuirlich &           \\  % <---
    \hhline{>{\arrayrulecolor{col2}}-%
            >{\arrayrulecolor{black}}-%
            >{\arrayrulecolor{col2}}-}
    \arrayrulecolor{black}
\rowcolor{col2} 
                        & Hybrid        &           \\
    \hhline{>{\arrayrulecolor{col2}}-%
            >{\arrayrulecolor{black}}-%
            >{\arrayrulecolor{col2}}-}
    \arrayrulecolor{black}
\rowcolor{col2}
\multirow{-3}{*}{dynamisch}
                        & Diskret       & \multirow{-3}{*}{Raum/Zeit}   \\
    \hhline{|---}
\cellcolor{col2} (Multi)-Agenten basiert
                        &   \multicolumn{2}{c}{}    \\
    \hhline{|-~~}
\end{tabular}
    \end{table}
\end{document}

Result is the same as in his answer.