To get the ; between author names you just need
\renewcommand{\multinamedelim}{\addsemicolon\space}
To get an ; instead of , & you just need:
\renewcommand{\finalnamedelim}{\multinamedelim}
Change last to family and first to given:
\DeclareNameAlias{sortname}{family-given} %Sort: Last name, first name
\DeclareNameAlias{default}{family-given} %Sort: Last name, first name
\renewcommand*{\mkbibnamefamily}[1]{\textsc{#1}}
and add the following code to get the closing dot for \fullcite:
\DeclareCiteCommand{\fullcite}
{\usebibmacro{prenote}}
{\usedriver
{\DeclareNameAlias{sortname}{default}}
{\thefield{entrytype}}}
{\multicitedelim}
{\usebibmacro{postnote}\adddot} % <===================================
Be sure to have
\preto\fullcite{\AtNextCite{\defcounter{maxnames}{3}}}
after the redefinition of \fullcite.
With the complete MWE
\RequirePackage{filecontents}
\begin{filecontents}{\jobname.bib}
@Book{Krugmann2015,
author = {Krugmann, Paul and Obstfeld, Maurice and Melitz, Mark J.},
title = {International economics: theory and policy},
year = {2015},
edition = {10. edition, global edition},
publisher = {Pearson},
location = {Boston },
isbn = {978-1-292-01955-7},
pubstate = {Massachusetts},
}
\end{filecontents}
\documentclass[a4paper,11pt,DIV=calc, titlepage]{scrartcl}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[ngerman]{babel}
\usepackage[%
left=4cm,right=2.5cm,top=2.0cm,bottom=2cm,
includeheadfoot
]{geometry}
\usepackage[babel, german=quotes]{csquotes}
\usepackage[%
style=authoryear-ibid,
natbib=true,
maxbibnames=3,
maxcitenames=2,
uniquelist=false,
uniquename=false,
backend=biber
]{biblatex}
\addbibresource{\jobname.bib}
\usepackage[hidelinks]{hyperref}
\renewcommand*{\mkbibnamefamily}[1]{\textsc{#1}} %Zitat und Lit in Kapitätlchen
\DefineBibliographyStrings{ngerman}{ % et al instead of "und" with 3 or more authors
andothers = {{et\,al\adddot}}, }
\renewcommand{\multinamedelim}{\addsemicolon\space} % <=================
\renewcommand{\finalnamedelim}{\multinamedelim} % <=====================
\DeclareNameAlias{sortname}{family-given} %Sort: Last name, first name
\DeclareNameAlias{default}{family-given} %Sort: Last name, first name
\DeclareFieldFormat[%
article,inbook,incollection,inproceedings,patent,thesis,unpublished,
report, norm, phdthesis, other, misc
]{citetitle}{#1} %Remove quotation marks from title
\DeclareFieldFormat[%
article,inbook,incollection,inproceedings,patent,thesis,unpublished,
report, norm, phdthesis, other, misc
]{title}{#1} %Remove quotation marks from title
\DeclareCiteCommand{\fullcite}
{\usebibmacro{prenote}}
{\usedriver
{\DeclareNameAlias{sortname}{default}}
{\thefield{entrytype}}}
{\multicitedelim}
{\usebibmacro{postnote}\adddot} % <===================================
%Fullcite change: Write out all authors up to 3
\preto\fullcite{\AtNextCite{\defcounter{maxnames}{3}}}
\begin{document}
I am a quote \parencite{Krugmann2015}.\\
Fullcite:\\
\fullcite{Krugmann2015}\\\\
\begingroup
\phantomsection\addcontentsline{toc}{section}{Literaturverzeichnis}
\printbibliography[title={Literaturverzeichnis}]
\endgroup
\end{document}
you will get the result:

EDIT:
Based on the comment of @moewe I changed the code for the fullcite to:
\makeatletter
\DeclareCiteCommand{\fullcite}
{\usebibmacro{prenote}}
{\usedriver
{\defcounter{maxnames}{\blx@maxbibnames}% Write out all authors up to 3
\DeclareNameAlias{sortname}{default}}
{\thefield{entrytype}}}
{\multicitedelim}
{\usebibmacro{postnote}\addperiod} % <===================================
\makeatother
Please see that command \preto\fullcite{\AtNextCite{\defcounter{maxnames}{3}}} is not longer needed. Because now \blx@maxbibnames (contains the given number 3 in the options for biblatex) is used, we need to enclose the code with \makeatletter and makeatother. The ending dot for the fullcite is now set by \addperiod.
With the following MWE (I deleted the \\ too)
\RequirePackage{filecontents}
\begin{filecontents}{\jobname.bib}
@Book{Krugmann2015,
author = {Krugmann, Paul and Obstfeld, Maurice and Melitz, Mark J.},
title = {International economics: theory and policy},
year = {2015},
edition = {10. edition, global edition},
publisher = {Pearson},
location = {Boston },
isbn = {978-1-292-01955-7},
pubstate = {Massachusetts},
}
\end{filecontents}
\documentclass[a4paper,11pt,DIV=calc, titlepage]{scrartcl}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[ngerman]{babel}
\usepackage[%
left=4cm,right=2.5cm,top=2.0cm,bottom=2cm,
includeheadfoot
]{geometry}
\usepackage[babel, german=quotes]{csquotes}
\usepackage[%
style=authoryear-ibid,
natbib=true,
maxbibnames=3,
maxcitenames=2,
uniquelist=false,
uniquename=false,
backend=biber
]{biblatex}
\addbibresource{\jobname.bib}
\usepackage[hidelinks]{hyperref}
\renewcommand*{\mkbibnamefamily}[1]{\textsc{#1}} %Zitat und Lit in Kapitätlchen
\DefineBibliographyStrings{ngerman}{ % et al instead of "und" with 3 or more authors
andothers = {{et\,al\adddot}}, }
\renewcommand{\multinamedelim}{\addsemicolon\space} % <=================
\renewcommand{\finalnamedelim}{\multinamedelim} % <=====================
\DeclareNameAlias{sortname}{family-given} %Sort: Last name, first name
\DeclareNameAlias{default}{family-given} %Sort: Last name, first name
\DeclareFieldFormat[%
article,inbook,incollection,inproceedings,patent,thesis,unpublished,
report, norm, phdthesis, other, misc
]{citetitle}{#1} %Remove quotation marks from title
\DeclareFieldFormat[%
article,inbook,incollection,inproceedings,patent,thesis,unpublished,
report, norm, phdthesis, other, misc
]{title}{#1} %Remove quotation marks from title
\makeatletter
\DeclareCiteCommand{\fullcite}
{\usebibmacro{prenote}}
{\usedriver
{\defcounter{maxnames}{\blx@maxbibnames}% Write out all authors up to 3
\DeclareNameAlias{sortname}{default}}
{\thefield{entrytype}}}
{\multicitedelim}
{\usebibmacro{postnote}\addperiod} % <===================================
\makeatother
\begin{document}
I am a quote \parencite{Krugmann2015}.
Fullcite:
\fullcite{Krugmann2015}
\begingroup
\phantomsection\addcontentsline{toc}{section}{Literaturverzeichnis}
\printbibliography[title={Literaturverzeichnis}]
\endgroup
\end{document}
you get the result:

\addperiodinstead of\addot. The former gives a full stop, the latter an abbreviation dot. While it is very unlikely that this will change things, it is semantically nicer to use\addperiod. The\preto\fullcitebit can be moved directly into the redefinition of\footcitesimilar to https://tex.stackexchange.com/a/399252/35864 – moewe Nov 08 '17 at 08:23sortnameanddefaulthave the same format, the\DeclareNameAlias{sortname}{default}in the definition of\fullciteshould not be needed any more. – moewe Nov 08 '17 at 15:25