When grouping images, there are defined sections. For
GSA, it is
"Observational", "Sketchbook/Development Work", and "Resolved/Finished Work". For
ECA, it is very similar with
"Observational/Development Work" and "Resolved/Finished Work" and from what I gather, five slides of "Inspiration" (work inspired by an artist, or an object or a subject matter).
For more details on how many slides you need for each of the sections, I suggest looking at the website as Fine Art and Design applications tend to differ (with the former requiring more slides).
As for
how much you should show, remember, this is only a
sample of what you can do. You do not need to put all of your work on it. As well as this, as I've mentioned before, the admissions team only spend 2-3 minutes per slide and they've got to look through hundreds of applications. If you have too many images on a slide, and their eye isn't drawn to any piece in particular, they may glaze over it entirely and miss some of your impressive pieces. You want to keep it clean and sharp, make an impression on the admissions team. Have faith in having one image slides; but also balance this with having slides that may have two or three images that complement each other.
As stillIII said, they do want to see that you're productive and self-motivated (through projects you've done yourself) but also they want to see that you are selective. So that means choosing work that displays your range in skill, but also making sure that it's of a decent quality and is relevant to your work.
In regards to whether the research to link to a finished piece, I think a mix is good. Show some of the finished pieces that have derived from your research and development work, as well as finished pieces that may be unrelated just to demonstrate your skill.
I hope I explained that well... Feel free to ask more questions or examples and I'll try and respond to the best of my ability on this.
[EDIT]
This is what I mean by some pieces working well on their own; and
others working well in a little group that complement one another. These two slides were included in my "Development" Section.