Fix spacing from sections in toc, and part title

Question

I've got to fix a friend's work that was done with latex. I've got almost all done, but there are a couple of issues that I couldn't fix, so I would like if you can help me please (an article document):

• He has 4 depth sectioning in the table of contents, from part to subsubsection. The problem is that part was in roman numbering and it leaves a big heading where it's displayed. I fixed the numbering, but I can't deal with the big heading. It's displayed like:

  1
  
  Planteamiento
  
  
  1.1 Introducción
  
  (content)
  

  and it's desired something like this:

  1 Planteamiento
  
  1.1 Introducción
  
  (content)
  

  but I can't find the command to rearrange the part title. I've tried to set part as section, section as subsection, subsection as subsubsection and subsubsection to paragraph. But he also uses paragraph and I got a bit mess. So I think the easiest way is to include part as kind of "supersection". So, is there a command to fix the big part title?

• As I've included part numbering in ToC, I had to fix section numbering to include part one. But now there is no space between the section numbers and the section name in the ToC. How can I add some space so they don't be so close?

EDIT: Here's my MWE:

\documentclass[12pt]{article}
\renewcommand{\thepart}{\arabic{part}}
\renewcommand{\thesection}{\thepart.\arabic{section}}
\renewcommand{\partname}{}

\makeatletter
\@addtoreset{section}{part}
\makeatother

\begin{document}
\tableofcontents
\newpage
\part{Big title}
\section{Lorem ipsum}
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor.

\section{Lorem ipsum 2}
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor.
\newpage
\part{Another big title}
\section{Section from big title 2}
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor.
\end{document}

Answer 1

The issue with the ToC entries can be fixed using \cftsetindents from the tocloft package; the issue with the part headings can be fixed with a redefinition (or a patching) of \@part

\documentclass[12pt]{article}
\usepackage{tocloft}

\renewcommand{\thepart}{\arabic{part}}
\renewcommand{\thesection}{\thepart.\arabic{section}}
\renewcommand{\partname}{}

\makeatletter
\@addtoreset{section}{part}
\def\@part[#1]#2{%
    \ifnum \c@secnumdepth >\m@ne
      \refstepcounter{part}%
      \addcontentsline{toc}{part}{\thepart\hspace{1em}#1}%
    \else
      \addcontentsline{toc}{part}{#1}%
    \fi
    {\parindent \z@ \raggedright
     \interlinepenalty \@M
     \normalfont
     \ifnum \c@secnumdepth >\m@ne
       \huge\bfseries\thepart\hskip0.5em
     \fi
     \huge\bfseries #2%
     \markboth{}{}\par}%
    \nobreak
    \vskip 3ex
    \@afterheading}
\makeatother

\cftsetindents{section}{0em}{2.3em}
\cftsetindents{subsection}{2.3em}{3em}
\cftsetindents{subsubsection}{5.3em}{3.3em}

\begin{document}
\tableofcontents
\newpage
\part{Test part}
\section{Test section}
\subsection{Test subsection}
\subsubsection{Test subsubsection}

\part{Test part}
\section{Test section}
\subsection{Test subsection}
\subsubsection{Test subsubsection}

\end{document}

An image of the ToC:

An image of the document body:

Here's the code in case you opt for the patching (the code is slightly shorter):

\documentclass[12pt]{article}
\usepackage{tocloft}
\usepackage{etoolbox}

\renewcommand{\thepart}{\arabic{part}}
\renewcommand{\thesection}{\thepart.\arabic{section}}
\renewcommand{\partname}{}

\makeatletter
\@addtoreset{section}{part}
\patchcmd{\@part}{\Large}{\huge}{}{}
\patchcmd{\@part}{\partname\nobreakspace\thepart}{\thepart\hskip0.5em}{}{}
\patchcmd{\@part}{\par\nobreak}{}{}{}
\makeatother

\cftsetindents{section}{0em}{2.3em}
\cftsetindents{subsection}{2.3em}{3em}
\cftsetindents{subsubsection}{5.3em}{3.3em}

\begin{document}
\tableofcontents
\newpage
\part{Test part}
\section{Test section}
\subsection{Test subsection}
\subsubsection{Test subsubsection}

\part{Test part}
\section{Test section}
\subsection{Test subsection}
\subsubsection{Test subsubsection}

\end{document}