Following suggestions by @moewe in the questions Enable "firstinits" in biblatex only for editors and Move names of editors followed by (Ed./Eds.) and a comma before title in biblatex, I have the code you see below. The problem here is that it prints a superfluous period after In when the collection has no editor, as seen in the Brekke entry.
\documentclass{article}
\usepackage[style = authoryear-comp]{biblatex}
\renewcommand*{\intitlepunct}{\space} % remove colon after "In:" for articles in books
%% Abbreviate first names of editors
\DeclareNameAlias{byeditor}{first-last-inits}
\DeclareNameFormat{first-last-inits}{%
\usebibmacro{name:first-last}{#1}{#4}{#5}{#7}%
\usebibmacro{name:andothers}}
%%
%% Move names of editors before the book title, and add "(Eds.)"
\usepackage{xpatch}
\DeclareNameAlias{editorin}{first-last-inits}
\newbibmacro*{byeditor:in}{%
\ifnameundef{editor}
{}
{\printnames[editorin]{editor}%
\addspace\bibsentence%
\mkbibparens{\usebibmacro{editorstrg}}%
\clearname{editor}%
\printunit{\addcomma\space}}}
\xpatchbibdriver{incollection}
{\usebibmacro{in:}%
\usebibmacro{maintitle+booktitle}%
\newunit\newblock
\usebibmacro{byeditor+others}}
{\usebibmacro{in:}%
\usebibmacro{byeditor:in}%
\setunit{\labelnamepunct}\newblock
\usebibmacro{maintitle+booktitle}%
\newunit\newblock
\usebibmacro{byeditor}}
{}{}
%%
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@INCOLLECTION{brekke1881,
AUTHOR = "K. Brekke",
BOOKTITLE = "Indbydelsesskrift til den offentlige examen i juni og juli 1881 ved Aars og Voss's latin- og realskole",
TITLE = "Bidrag til dansk-norskens lydl{\ae}re",
YEAR = "1881",
LOCATION = "Kristiania",
PAGES = "1--66",
PUBLISHER = "W. C. Fabritius"}
@INCOLLECTION{jahr2007,
AUTHOR = "Ernst H{\aa}kon Jahr",
BOOKTITLE = "{\AA} sj{\aa} samfunnet gjennom spr{\aa}ket",
EDITOR = "Gunnstein Akselberg and Johan Myking",
TITLE = "Bruk av omgrepa 'standardtalem{\aa}l', 'normalisering' og 'knot' for {\aa} skildre spr{\aa}ktilh{\o}va i Noreg i dag",
YEAR = "2007",
LOCATION = "Oslo",
PAGES = "93--98",
PUBLISHER = "Novus"}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
\nocite{*}
\printbibliography
\end{document}

Another option is to follow the suggestion by @Guido (also to my question Move names of editors followed by (Ed./Eds.) and a comma before title in biblatex), and use the code below. The problem here is that the first names of the editors are not abbreviated (naturally enough, since I didn't ask for it in connection with that question).
\documentclass{article}
\usepackage[style = authoryear-comp]{biblatex}
\renewcommand*{\intitlepunct}{\space} % remove colon after "In:" for articles in books
%% Move names of editors before the book title, and add "(Eds.)"
\usepackage{xpatch}
\xpatchbibmacro{editorstrg}{\bibstring}{\bibcpstring}{}{}
\renewbibmacro*{in:}{
\ifentrytype{incollection}{%
\DeclareNameAlias{editor}{first-last}
\printtext{In}
\ifnameundef{editor}
{}
{\printnames{editor}%
\addspace
\mkbibparens{\usebibmacro{editorstrg}}
\setunit{\addcomma\addspace}%
}%
\printfield[book]{booktitle}
\clearfield{booktitle}
\clearname{editor}
}
{}%
}%%
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@INCOLLECTION{brekke1881,
AUTHOR = "K. Brekke",
BOOKTITLE = "Indbydelsesskrift til den offentlige examen i juni og juli 1881 ved Aars og Voss's latin- og realskole",
TITLE = "Bidrag til dansk-norskens lydl{\ae}re",
YEAR = "1881",
LOCATION = "Kristiania",
PAGES = "1--66",
PUBLISHER = "W. C. Fabritius"}
@INCOLLECTION{jahr2007,
AUTHOR = "Ernst H{\aa}kon Jahr",
BOOKTITLE = "{\AA} sj{\aa} samfunnet gjennom spr{\aa}ket",
EDITOR = "Gunnstein Akselberg and Johan Myking",
TITLE = "Bruk av omgrepa 'standardtalem{\aa}l', 'normalisering' og 'knot' for {\aa} skildre spr{\aa}ktilh{\o}va i Noreg i dag",
YEAR = "2007",
LOCATION = "Oslo",
PAGES = "93--98",
PUBLISHER = "Novus"}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
\nocite{*}
\printbibliography
\end{document}

So my question is: How can I modify the suggestion by @moewe to get rid of the unwanted period in case of missing editors, or how can I modify the suggestion by @Guido to abbreviate the first names of editors?

\printunitfor\intitlepunctin thein:bibmacro might help:\renewbibmacro*{in:}{\printtext{\bibstring{in}}\printunit{\intitlepunct}}. (I will investigate this properly tomorrow though.) – moewe Sep 02 '14 at 21:36\DeclareNameAlias{editor}{first-last}to\DeclareNameAlias{editor}{first-last-inits}and copying\DeclareNameFormat{first-last-inits}{\usebibmacro{name:first-last}{#1}{#4}{#5}{#7}\usebibmacro{name:andothers}}to that document should help (untested, but I should think it does the job). That is, you should be able to apply the answer to Enable “firstinits” in biblatex only for editors here as well, but the name format in question iseditor, notbyeditor(so we have to change that). – moewe Sep 02 '14 at 21:43(ed.),with a lowercaseeinstead of(Ed.),when there is only one editor. I've put a comment about that to his answer. – Sverre Sep 03 '14 at 11:30(Eds.),, where rather the main title should be. I'll await the fix for your own code, then:). – Sverre Sep 03 '14 at 11:59