Note that this is unusual. It would be better to not use such a small headsep.
But if you really want to do this, you can use
\usepackage{xpatch}
\xpretocmd\sectionlinesformat{\vspace*{0pt}}{}{\PatchFailed}
Then the beforeskip is also inserted if the section titles (section, subsection etc.) are on top of a new page.

Additional remarks:
Do not set \parskip manually. Use the KOMA-Script option parskip=half- instead.
Replace \clearscrheadfoot by \clearpairofpagestyles. With both commands \cfoot[]{} is not needed. And if both the optional and the mandatory argument of \ifoot etc. are equal you can use the starred version.
To restart the page numbering use \pagenumbering and insert a \cleardoublepage or \cleardoubleoddpage before this command to ensure that it is excecuted on a righthand page.
Code:
\documentclass[11pt,twoside,english,openright, bibliography=totoc,
parskip=half-
]{scrreprt}
\usepackage{helvet}
\renewcommand{\familydefault}{\sfdefault}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\usepackage[a4paper]{geometry}
\geometry{verbose,margin=2.5cm,lmargin=2.75cm,headheight=18pt,headsep=8pt,footskip=26pt}
\setcounter{secnumdepth}{3}
\setcounter{tocdepth}{3}
\usepackage{verbatim}
\usepackage{setspace}
\usepackage[authoryear]{natbib}
\onehalfspacing
\makeatletter
\usepackage{lscape}
\usepackage[automark, headsepline, footsepline, plainfootsepline]{scrlayer-scrpage}
\pagestyle{scrheadings}
\automark[chapter]{chapter}
\clearpairofpagestyles
\ohead{\headmark}
\ifoot*{Test}
\ofoot*{\pagemark}
\usepackage{pdfpages}
\RedeclareSectionCommand[beforeskip=12pt,afterskip=12pt]{chapter}
\setkomafont{chapter}{\sffamily\LARGE}
\RedeclareSectionCommand[beforeskip=-12pt,afterskip=10pt]{section}
\RedeclareSectionCommands[beforeskip=-12pt,afterskip=8pt]{subsection,subsubsection,paragraph}
\setkomafont{paragraph}{\sffamily\normalsize}
\usepackage{xpatch}
\xpretocmd\sectionlinesformat{\vspace*{0pt}}{}{\PatchFailed}
\usepackage{blindtext}% only for dummy text
\setkeys{Gin}{width=\textwidth}% default width for \includegraphics
\raggedbottom
\usepackage{babel}
\usepackage[hyphens]{url}
\usepackage[colorlinks=true, urlcolor=blue, linkcolor=black,citecolor=black]{hyperref}
\begin{document}
\pagenumbering{roman}
\chapter{Introduction}
\Blindtext
\cleardoubleoddpage
\pagenumbering{arabic}
\chapter{A Chapter}
\section{This is a Section}
\blindtext
\blindtext
\blindtext
\blindtext
\section{A Second Section}
\subsection{This is a Sub-section}
\blindtext
\section{A Second Section}
\subsection{This is a Sub-section}
\Blindtext
\end{document}
If you want to use a smaller skip before section titles on a new page than the normal beforeskip, you can use something like
\usepackage{xpatch}
\makeatletter
\xpatchcmd\sectionlinesformat
{\@hangfrom{\hskip #2#3}{#4}}
{\parbox[b]{\textwidth}{\vspace*{7pt}\raggedsection\@hangfrom{\hskip #2#3}{#4}}}
{}{\PatchFailed}
\makeatother
But then you have to decrease the beforeskip by the same length. In the example beforeskip would be 12pt-7pt=5pt.
\RedeclareSectionCommand[beforeskip=-5pt,afterskip=10pt]{section}
\RedeclareSectionCommands[beforeskip=-5pt,afterskip=8pt]{subsection,subsubsection,paragraph}

Code:
\documentclass[11pt,twoside,english,openright, bibliography=totoc,
parskip=half-
]{scrreprt}
\usepackage{helvet}
\renewcommand{\familydefault}{\sfdefault}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\usepackage[a4paper]{geometry}
\geometry{verbose,margin=2.5cm,lmargin=2.75cm,headheight=18pt,headsep=8pt,footskip=26pt}
\setcounter{secnumdepth}{3}
\setcounter{tocdepth}{3}
\usepackage{verbatim}
\usepackage{setspace}
\usepackage[authoryear]{natbib}
\onehalfspacing
\makeatletter
\usepackage{lscape}
\usepackage[automark, headsepline, footsepline, plainfootsepline]{scrlayer-scrpage}
\pagestyle{scrheadings}
\automark[chapter]{chapter}
\clearpairofpagestyles
\ohead{\headmark}
\ifoot*{Test}
\ofoot*{\pagemark}
\usepackage{pdfpages}
\RedeclareSectionCommand[beforeskip=12pt,afterskip=12pt]{chapter}
\setkomafont{chapter}{\sffamily\LARGE}
\RedeclareSectionCommand[beforeskip=-5pt,afterskip=10pt]{section}
\RedeclareSectionCommands[beforeskip=-5pt,afterskip=8pt]{subsection,subsubsection,paragraph}
\setkomafont{paragraph}{\sffamily\normalsize}
\usepackage{xpatch}
\makeatletter
\xpatchcmd\sectionlinesformat
{\@hangfrom{\hskip #2#3}{#4}}
{\parbox[b]{\textwidth}{\vspace*{7pt}\raggedsection\@hangfrom{\hskip #2#3}{#4}}}
{}{\PatchFailed}
\makeatother
\usepackage{blindtext}% only for dummy text
\setkeys{Gin}{width=\textwidth}% default width for \includegraphics
\raggedbottom
\usepackage{babel}
\usepackage[hyphens]{url}
\usepackage[colorlinks=true, urlcolor=blue, linkcolor=black,citecolor=black]{hyperref}
\begin{document}
\pagenumbering{roman}
\chapter{Introduction}
\Blindtext
\cleardoubleoddpage
\pagenumbering{arabic}
\chapter{A Chapter}
\section{This is a Section}
\blindtext
\blindtext
\blindtext
\blindtext
\section{A Second Section}
\subsection{This is a Sub-section}
\blindtext
\section{A Second Section}
\subsection{This is a Sub-section}
\Blindtext
\end{document}