As many understand socialism it is first and foremost a political ideology that is deeply rooted in economical theory.  In general that is not any different from other political ideologies.  

That said socialism is in essence the equal distribution of wealth in society and that has to be done by taking control over the means of production, that is advocating a specific economic system although in different degrees (some people advocate taking absolute control over the means of production others advocate just taking partial, even minimal, control over the means of production: Communism/Marxism vs. Social Democracy).

There are no countries that are members of the Socialist International, only political parties.    

And yes, I believe it is possible to have a socialist party advocating and executing socialist policies within a pluralistic political system that have a mixed or capitalist economical system.  You just have to be able and willing to differentiate between a political system and the economic system even if the two systems are interdependent.  
 

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