How to verify if entry `country = {}` is empty in a custom BibLaTeX library?

You should check whether the field exists as part of the \DeclareCiteCommand using \iffieldundef (or something similar; see section 4.6.2 Stand-alone Tests in the biblatex documentation):

\DeclareCiteCommand{\citecountry}
  {\boolfalse{citetracker}%
   \boolfalse{pagetracker}%
   \usebibmacro{prenote}}
  {\iffieldundef{country}{}{(\printtext{\printfield{country}})}}
  {\multicitedelim}
  {\usebibmacro{postnote}}

and here is \printcontrib:

\newcommand{\printcontrib}[1]{%
  \citeauthor*{#1}, 
  \citetitle*{#1}, 
  \citeevent{#1},
  \citecity{#1} 
  \citecountry{#1},
  \citedate{#1} (\citeyear{#1})
} 

You may also write a larger \DeclareCiteCommand rather using \printcontrib.

In biblatex, field formatting such as brackets or emphasis or italics should not be written into the macro directly in most cases, they should be achieved with \DeclareFieldFormat. That way you make sure that biblatex can properly detect empty fields and do nothing in that case.

You could just do

\DeclareFieldFormat{country}{\mkbibparens{#1}}

\DeclareCiteCommand{\citecountry}
  {\boolfalse{citetracker}%
   \boolfalse{pagetracker}%
   \usebibmacro{prenote}}
  {\printfield{country}}
  {\multicitedelim}
  {\usebibmacro{postnote}}

The field is then wrapped in brackets whenever it is shown and ignored otherwise. Note that there is no need to wrap a single \printfield into a \printtext without argument, \printfield{country} will do the same as \printtext{\printfield{country}}.

Instead of defining \citecontrib as you do now, you should probably just define a bibliography driver for @contribution like so (this is just a first rough shot at this, but you get the idea)

\DeclareFieldFormat{country}{\mkbibparens{#1}}
\DeclareFieldFormat[contribution]{title}{\mkbibemph{#1}}

\newbibmacro*{event+venue+city+country+date}{%
  \printfield{eventtitle}%
  \newunit
  \printfield{eventtitleaddon}%
  \newunit
  \printeventdate
  \newunit
  \printfield{city}
  \setunit{\addspace}%
  \printfield{country}
  \newunit}

\DeclareBibliographyDriver{contribution}{%
  \usebibmacro{bibindex}%
  \usebibmacro{begentry}%
  \usebibmacro{author/editor+others/translator+others}%
  \setunit{\printdelim{nametitledelim}}\newblock
  \usebibmacro{title}%
  \newunit
  \printlist{language}%
  \newunit\newblock
  \usebibmacro{byauthor}%
  \newunit\newblock
  \usebibmacro{event+venue+city+country+date}%
  \newunit\newblock
  \printfield{howpublished}%
  \newunit\newblock
  \printfield{note}%
  \newunit\newblock
  \usebibmacro{location+date}\printdate%
  \newunit\newblock
  \iftoggle{bbx:url}
    {\usebibmacro{url+urldate}}
    {}%
  \newunit\newblock
  \usebibmacro{addendum+pubstate}%
  \setunit{\bibpagerefpunct}\newblock
  \usebibmacro{pageref}%
  \newunit\newblock
  \iftoggle{bbx:related}
    {\usebibmacro{related:init}%
     \usebibmacro{related}}
    {}%
  \usebibmacro{finentry}}

Then you can just use \fullcite and you are done.