First off, I have not created any of these so can only speculate.
Yes.
The few ChatGPT plugins that I have tried read the entire PDF, however many only read the text as trying to extract data from the math expressions and graphs is beyond their capability. This is do to the fact that a PDF is designed for layout and presentation and not context extraction or passing along knowledge as a data interchange format.
Not sure exactly what you mean by that but from I understand they embed the knowledge into a vector database and then use the prompt to pick out the relevant parts and compose a reply.
The analogy I use to explain to others for how to understand the concept is instead of focusing on the idea of a PDF instead think about the ideas the author(s) of the paper are trying to pass along in the paper and that you are conversing with them.
If you can run plugins with ChatGPT then at this site
search for PDF or paper and try some. The two main differences I find in them is that many will read a single PDF, (https://pugin.ai/p/chatwithpdf) while this one (https://pugin.ai/p/science) will pick the relevant papers out 250M scientific papers.
LangChain has this
https://github.com/mayooear/gpt4-pdf-chatbot-langchain
and there are similar repos on GitHub (ref), YMMV.
Here is a specific use case for such technology for those that think such would be limited to just academics.