fontsize
According to LyX Wiki, I can define my font size by means of this code (in case of 10.5pt) :
\usepackage{type1cm}
\renewcommand\normalsize{%
\@setfontsize\normalsize{10.5pt}{12pt}
\abovedisplayskip 10\p@ \@plus2\p@ \@minus5\p@
\abovedisplayshortskip \z@ \@plus3\p@
\belowdisplayshortskip 6\p@ \@plus3\p@ \@minus3\p@
\belowdisplayskip \abovedisplayskip
\let\@listi\@listI}\normalsize
But how can I calculate this value in case of 14pt, 16pt, 18pt?
There's no font selection scheme in Plain TeX. There are some packages that provide an infrastructure:
If you need to match fonts used in LaTeX, use LaTeX.
One should also keep in mind that scaling the Computer Modern fonts is not a good practice.
Here are two samples; the first has "A test" printed with
The second sample is of "A test" printed with \tiny from LaTeX (class article at 10pt size):
It's clear that the third option in the first sample corresponds to \tiny.
Generally you are best off using the mechanisms offered by the document class and standard size commands for fonts. The subsubsection font in your example is the same size as the normal text, if you want it bigger, trying using \large. In the KOMA classes you do this via \setkomafont, e.g.
\setkomafont{subsubsection}{\normalfont\large}
or if you only want to change the size and not the style
\addtokomafont{subsubsection}{\large}
If you wished to set the font size explicitly then it would be
\setkomafont{subsubsection}{\normalfont\fontsize{14}{16}\selectfont}
or
\addtokomafont{subsubsection}{\fontsize{14}{16}\selectfont}
Note the arguments to \fontsize are just numbers (denoting pointsizes) not dimensions, the second number should be larger than the first, it indicates the line skip to be used for this font. The basic font size for the document is specified by the a fontsize option to the documentclass, e.g.
\documentclass[fontsize=12pt]{scrartcl}
As other have said you should not use fancyhdr or titlesec. For your purposes the latter is replaced by simple \setkomfont commands, the former by the scrlayer-scrpage package.
As regards the geometry package, in your case you seem to want to specify the margins precisely, in which case using this package is the only option.
Here is an implementation of some of these things in your example.
\documentclass[twoside,parskip=half,numbers=noendperiod,abstract=true]{scrartcl}
\usepackage[british]{babel}
\bibliographystyle{nature}
\usepackage[utf8]{inputenc}
\usepackage{microtype,textcomp}
\usepackage[a4paper,left=25mm,right=25mm,top=25mm,bottom=25mm,
headsep=10mm]{geometry}
\usepackage{multicol}
\usepackage{hyperref}
\usepackage{paralist}
\renewcommand*{\thesection}{\Roman{section}.}
\renewcommand*{\thesubsection}{\arabic{subsection}}
\setkomafont{title}{\normalfont\bfseries}
\setkomafont{subtitle}{\normalfont\Large\bfseries}
\setkomafont{subsection}{\normalfont\large\bfseries}
\setkomafont{subsubsection}{\normalfont\large}
\setkomafont{author}{\large}
\usepackage{scrlayer-scrpage}
\pagestyle{scrheadings}
\ihead{}\ohead{}\chead{\headmark}
\setkomafont{pageheadfoot}{\normalfont}
\markboth{Title \textbullet{} Course \textbullet{} 2014}{Title \textbullet{}
Course \textbullet{} 2014}
\title{Title}
\subtitle{Subtitle}
\author{\textsc{Name Surname}\\[2ex]
\normalsize University name \\
\normalsize \href{mailto:name@domain.com}{name@domain.com}}
\date{}
\begin{document}
\maketitle
\thispagestyle{scrheadings}
\unskip\vspace{-1.5\baselineskip}
\begin{abstract}
Ut venenatis sodales leo et imperdiet. Pellentesque sagittis
volutpat feugiat. Nunc in dictum libero. Sed sed dui leo. Curabitur
condimentum laoreet metus vitae tempus. Vestibulum id feugiat risus,
ac feugiat libero. Mauris ultricies eget risus et venenatis. Donec
gravida mauris sed interdum vulputate. Morbi nunc quam, finibus
vitae tincidunt a, vulputate eget sapien.
\end{abstract}
\begin{center}
\textbf{Keywords}: keyword 001 \textperiodcentered{} keyword 002
\textperiodcentered{} keyword 003 \textperiodcentered{} keyword 004
\end{center}
\medskip
\begin{multicols}{2}
\section{Section 1}
Vestibulum vel ipsum vel urna iaculis tincidunt ut eu arcu. Etiam in
ante dui. Suspendisse porta lacus et facilisis suscipit. Donec congue
egestas nunc, ut ullamcorper felis ultricies ut. Vivamus eu lorem
risus. Vivamus sollicitudin bibendum ornare. Duis dignissim metus sed
eleifend posuere. In consequat aliquet sapien, at faucibus ipsum.
\section{Section 2}
\subsection{Sub-section 1}
\subsubsection{Sub-subsection}
Aliquam ultricies eleifend bibendum. Pellentesque eu augue
orci. Integer ut dolor aliquet enim semper aliquam. Suspendisse sit
amet volutpat ex. Pellentesque lacinia dignissim molestie. Cras
consectetur efficitur purus, id viverra enim tincidunt quis. Morbi sed
blandit nulla, eu sodales purus. Aenean nec semper risus. Sed
malesuada finibus tellus vitae eleifend. Etiam ut cursus ipsum, ac
faucibus ligula. Morbi non est sed ligula fringilla finibus. Sed
interdum euismod ex nec tincidunt. Pellentesque ut ipsum enim. Quisque
aliquet dolor ac lectus congue, nec pellentesque metus
eleifend. Nullam sit amet lacus nulla.
\subsubsection{Sub-section 2}
Phasellus commodo augue vitae enim interdum, et tincidunt leo
consectetur. Sed in mi sit amet velit aliquet dapibus. Phasellus ut
massa a arcu aliquam rhoncus ultricies quis mi. Cras a tortor
egestas, luctus purus a, mollis lacus. Mauris eget molestie neque,
dapibus lobortis ligula. Sed id luctus tortor. Donec elementum lacus
vitae tincidunt imperdiet. Praesent in facilisis ligula. Nam
venenatis sed eros quis consequat. Maecenas sit amet eros sed purus
convallis pretium. Suspendisse potenti. Cras sed ultricies
diam. Nullam feugiat scelerisque leo vitae facilisis. Praesent quis
felis ante. Aenean in justo magna.
\end{multicols}
\end{document}
In answer to additional points in the comments
to get a line under the header use headsepline=true either as a document option or perhaps better as
\KOMAoptions{headsepline=true}
where you are defining the heading style
to increase the space to footnotes, use the footnotsep option of the geometry package. This is equivalent to setting \skip\footins, but keeps your page specification in one place.
the title element has size \huge by default and the above font changing commands do not affect this.
Best Answer
Note that defining the font size manually like this is not the normal way to do it and only for advanced users. You should use a package or class for changing the font size globally. If you simply want a larger font use
\large,\Large,\LARGE,\huge, or\Huge. With LaTeX it is not common to specify the font size of a piece of text in points.You can set the default (global) font size by using the
10pt,11ptor12ptclass options. For more font sizes see the following threads:Making default font size 16pt
How to specify font size less than 10pt (or more than 12pt)?