“Three questions at a time – that’s truly impossible!”
Note: I use TeXnicCenter version 2.0 alpha4.
Regarding 1.) No, there is no button or key shortcut, as far as I see. But you can navigate in the output window with cursors or with the keys PgUp / PgDn or even better with the combination Ctrl+Home / Ctrl+End and then use the error buttons or the appropriate F9 / Shift+F9 keys. See also the window, that you get with Ctrl+Alt+R. Note for users with non-english keyboards: If you have a AltGr key – it does not work!
Reg 2.) You mix up “1” and “l”. It’s the abbreviation for “line”, not the cipher.
Reg. 3.) Don’t blame TeXnicCenter here: Usually it sets the cursor in the line, where the output routine of LaTeX (or whatever you used) the error noticed. It will be the line you see in the output window. That the causing error sometimes is hard to catch, is known in (La)TeX, compare for instance the answers to Documents with typical LaTeX errors or take a look on this example:
\documentclass{article}
\usepackage[latin,english]{babel} % needed for "blindtext",
% "english" is the active language
\usepackage{blindtext,lipsum} % just for the examples
\usepackage{refcount}
\usepackage[%
colorlinks=true,%
]{hyperref}
\newcommand{\mypageref}[2]{\hyperref{./\jobname.pdf}{page}{\getpagerefnumber{#1}}{#2}}
% \mypageref{<label>}{some linked text}
\begin{document}
\section{Package \texttt{blindtext} with Latin blindtext}\label{btext-la}
Compare package \hyperref[lipsum]{\ttfamily lipsum} on
\mypageref{{lipsum}page \pageref*{lipsum}}.
% no error with correct brace placement:
%\mypageref{lipsum}{page \pageref*{lipsum}}.
\medskip
\begin{otherlanguage}{latin}
\blindtext[1]
\end{otherlanguage}
\newpage
\section{Package \texttt{lipsum}}\label{lipsum}
Compare package \hyperref[btext-la]{\texttt{blindtext} with pseudo-Latin text} on
\mypageref{btext-la}{page \pageref*{btext-la}.
\medskip
\begin{otherlanguage}{latin}
\lipsum[1]
\end{otherlanguage}}
\end{document}
(Code originally from Using \hyperlink to link text to page with an implicit page anchor not known in advance)