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}

letnc=nullcell                                                  % Shortcuts
letsc=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
defcals@framers@width{0.4pt}   % Outside frame horizontal rules
defcals@framecs@width{0.4pt}   % Outside frame horizontal rules, reduce
                                 % thickness if you find them too heavy
cals@setpadding{Ag}
cals@setcellprevdepth{Al}
defcals@cs@width{0.4pt}        % Inside rules, reduce if the rule is too heavy
defcals@rs@width{0.4pt}
defcals@bgcolor{}              % Define cals@bgcolor to empty

defgreen{ifxcals@bgcolorempty      % Colour switch (on-off)
    defcals@bgcolor{darkGreen}
else defcals@bgcolor{} fi}

deflgreen{ifxcals@bgcolorempty     % Colour switch (on-off)
    defcals@bgcolor{lightGreen}
else defcals@bgcolor{} fi}

deftb{ifxcals@borderTrelax     % Top border switch (off-on)
    defcals@borderT{0pt}
else letcals@borderTrelaxfi}

defbb{ifxcals@borderBrelax     % Botton border switch (off-on)
    defcals@borderB{0pt}
else letcals@borderBrelaxfi}

defrb{ifxcals@borderRrelax     % Right border switch (off-on)
    defcals@borderR{0pt}
else letcals@borderRrelaxfi}

% R1 Body
brow
    greenalignCcell{Modell-Überkategorien}green
    tbrbnc{lt}
    nc{rt}tbrb
erow
% R2 Body
brow
    cell{statisch}
    rbnc{l}
    nc{r}rb
erow
% R3 Body
brow
    cell{zufällig (Monte-Carlo)}
    rbnc{lb}
    nc{rb}sc{}rb
erow
% R4 Body
brow
    lgreennc{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
    rbbbnc{ltb}
    nc{rtb}sc{}bbrb
erow
makeatletter
end{calstable}par % par needed to align the tabular

end{document}