I will answer the last question first. Content specifically created for V4 should fit any of her other morphs like Stephanie 4, The Girl 4, etc unless otherwise noted on the webpage. And even if these morphs do not exist, you can transfer morphs to content from within PP2014.

Genesis/Genesis 2 are quite different; their mesh is low res and designed to be morphed into many different characters and creatures. And their UVs can be interchanged to accept many textures from the morph iterations. However, installation is tricky and can become problematic if installs are incorrect. Before you begin, you need to install the DSON importer into your main Poser folder. This app will bring Genesis/Genesis 2 into Poser. Next, you will need to install both Poser CF and DAZ CF and link both to your PP2014 Library. The reason for both file types to be linked to Poser, DSON calls on the DAZ content for Poser importation. If these files are not available, you will get an empty scene. Some individuals create 2 separate content folders, one for Poser runtime and another for DAZ content. Others place both type of files into one content folder and just link that to the Poser Library.

http://docs.daz3d.com/doku.php/public/software/dson_importer/poser/userguide/dson_installation_requirements/tutorials/dson_installation/start

http://docs.daz3d.com/doku.php/public/software/dson_importer/poser/userguide/dson_importer_usage/tutorials/using_dson_importer/start

The above links give an overview on how to install and use DSON Importer. I would suggest that you put off using Genesis/Genesis 2 for the meantime and concentrate on the Generation 4 figures just to learn the software. Getting involved with Genesis/Genesis 2 too early will lead to frustration.