paragraph style - how to force line break? \paragraph{} \\ - make paragraph a header?

You didn't say anything about your document class. So, here comes an example for article that uses the titlesec package.

\documentclass[11pt,a4paper,english]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage[raggedright]{titlesec}
\usepackage{blindtext}

\titleformat{\paragraph}[hang]{\normalfont\normalsize\bfseries}{\theparagraph}{1em}{}
\titlespacing*{\paragraph}{0pt}{3.25ex plus 1ex minus .2ex}{0.5em}

\begin{document}
  \blinddocument
\end{document}

You can easily adjust the space before and after the heading according to your needs. The package manual has the details. The package also masters page styles so that it might not be necessary to load fancyhdr.

Note that the blindtext package is only used for creating dummy text thus not part of the solution.

With the default settings, your request would render exactly like a \subsubsection*, so maybe you could just use that instead of \paragraph?

I have seen many hacks for this, including \mbox{} and other approaches but this one is the most convenient!

\paragraph ~\\

Source for the answer