[Tex/LaTex] \textbf{} does not work

Question

When I write in \gre \textbf{} does not work, but when I write in \lat everything is in bold and I cannot convert it to normal with {\normalfont }
I use an assignment template from ShareLatex:

%%% Template originaly created by Karol Kozioł (mail@karol-koziol.net) and modified for ShareLaTeX use

\documentclass[a4paper,11pt]{article}

\usepackage[english,greek]{babel}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{graphicx}
\usepackage{xcolor}
\usepackage{tgtermes}
\usepackage{amsfonts}

newcommand{\lat}{\selectlanguage{english}}
\newcommand{\gre}{\selectlanguage{greek}}

\usepackage[
pdftitle={Math Assignment}, 
pdfauthor={Joe Doe, Some University},
colorlinks=true,linkcolor=blue,urlcolor=blue,citecolor=blue,bookmarks=true,
bookmarksopenlevel=2]{hyperref}
\usepackage{amsmath,amssymb,amsthm,textcomp}
\usepackage{enumerate}
\usepackage{multicol}
\usepackage{tikz}

\usepackage{geometry}
\geometry{total={210mm,297mm},
left=25mm,right=25mm,%
bindingoffset=0mm, top=20mm,bottom=20mm}


\linespread{1.3}

\newcommand{\linia}{\rule{\linewidth}{0.5pt}}

% custom theorems if needed
\newtheoremstyle{mytheor}
{1ex}{1ex}{\normalfont}{0pt}{\scshape}{.}{1ex}
{{\thmname{#1 }}{\thmnumber{#2}}{\thmnote{ (#3)}}}

\theoremstyle{mytheor}
\newtheorem{defi}{Definition}

% my own titles
\makeatletter
\renewcommand{\maketitle}{
\begin{center}
\vspace{2ex}
{\huge \textsc{\@title}}
\vspace{1ex}
\\
\linia\\
\@author \hfill \@date
\vspace{4ex}
\end{center}
}
\makeatother
%%%

% custom footers and headers
\usepackage{fancyhdr,lastpage}
\pagestyle{fancy}
\lhead{}
\chead{}
\rhead{}
%\lfoot{Assignment \textnumero{} 5}
%\cfoot{}
%\rfoot{Page \thepage\ /\ \pageref*{LastPage}}
\renewcommand{\headrulewidth}{0pt}
%\renewcommand{\footrulewidth}{0pt}
%

%%%----------%%%----------%%%----------%%%----------%%%

For example {\gre \textbf{Άσκηση}} and {\lat exercise}

Answer 1

I don't really know if tgtermes even has a bold variant of Greek font (if so, you're better off with the computer modern variant, as searching for the right templates of such peculiar fonts is pretty much the definition of masochism). Since you didn't specify the necessity of a specific font, I think my answer should suffice. You will probably dislike the change of font, but when you see all the vast options that come with it (and would probably induce some errors when paired with other fonts) you might reconsider.

The code.

\documentclass[a4paper,11pt]{article}

\usepackage[english,greek]{babel}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}

\newcommand{\lat}{\selectlanguage{english}}
\newcommand{\gre}{\selectlanguage{greek}}

\begin{document}

\setlength{\parindent}{0cm}

{\lat It works!} \\
{\lat \textbf{It works!}} \\
{\lat \textit{It works!}} \\
{\lat \textbf{\textit{It works!}}} \\\\
{\gre It works!} \\
{\gre \textbf{It works!}} \\
{\gre \textit{It works!}} \\
{\gre \textbf{\textit{It works!}}}

\end{document}

The result.