Hello!
The related article plugin is meant to work after a certain number of paragraphs. That means that articles that will receive the 'related articles in content' output must have a certain number of paragraphs in the content, ie <p> tags. If the content has 4 paragraphs and you set the module instance of Latest News Enhanced Pro (LNEP) to show after the 5th, for instance, the related articles won't show.
What you are trying to do (adding related articles at the end of articles) can be done differently if you have a template position available under the content. In that case, do not use the plugin but use LNEP in that position of the template and use the module instance normally by using the 'Use as related' parameter.
'Related by ' options are limited to what is possible to do in the database query. 'Match at least 2 tags', for instance, is impossible to do in the query and would require extra processing after the request has been returned, with poor performance. That is why that option is not offered.
Consider this: when using the related feature, you are trying to match one article with all the others in the database (hopefully narrowed down to some categories to limit the search), which requires intensive processing time.
Finally, the plugin 'related articles in content' ONLY sets the module in a specific position of an article content. All regular parameters (such as layout) are independent of the plugin and are set by the module. Therefore, if the module instance you have created 'works' in a simple template position (in your trials), it will work with the plugin.
Hope this helps!
Olivier.