In Joyce's "Eveline," no, Eveline is not going to Argentina to be a prostitute. Why would you think that? Is that what you think of when you think of Argentina? There is nothing whatsoever in the story about Eveline going into prostitution. She is a 19-year-old woman with a lousy life who meets a sailor and wants to go away.
The importance of the photo is that the priest pictured is one more person to add to the list of people who have left Ireland. The story is filled with people who leave Ireland, and that is what Eveline wants to do.
The photo is described as yellow because it's deteriorated; it's old. And of course this, by extension, suggests the state of Ireland itself.