Whatever grants (e.g., if I wanted to apply for a fellowship) are out of the questions as they are seen as a "parallel move." The next 'big' thing will be to help him in the grant writing process (e.g., collect CVs from collaborators, supervise grad students on editing these CVs, coming up with roles for who is going to do what etc.). Are these tasks the norm for a postdoc? I, personally, would like to get hands on experience in the actual writing. Maybe those will come at some point.
I thought that the administrative people will take care of things, such as contact forms for x collaborator, travel forms, reserve room for x talk etc. Are these also the norm for a postdoc to do? I am asking because I never discussed upfront some of these tasks and now they keep coming and take most of my time.
I just wanted to comment that I don't see you applying for fellowships as a parallel move. You might be listed as an NIH Postdoctoral Fellow in title, but you did not write and receive that grant. I would suggest that you consider applying for independent postdoctoral fellowship funding if your PI approves.
In regard to collecting information for the grant proposal -- does this mean you are going to be listed as a collaborator on the grant proposal? It would be nice if you were, but I don't know how common that is. It would also be nice if, as you say, you had experience writing the proposal. As for only collecting materials, this task would be a valuable learning experience for you on how to format CV's and what this type of information looks like. I would not denigrate this idea.
Overall, it looks like your thoughts about a lot of this process as a postdoc are on track. The one thing I would I would advise is to find someone other than your PI who can give you advice -- preferably not one of his close friends or collaborators. If you are interested in a TT job, I also suggest you mentor yourself.
These books and the video are really great: http://www.hhmi.org/resources/labmanagement/moves.html
There are many other books out there on how to be successful and land a TT job.
I also don't think you should worry about the office shared with a graduate student and having to organize your collaborators' visit. These are very common tasks that a postdoc has to do / has to deal with. I organized the agenda/food for our collaborators visiting last week, I'm handling all of the hiring paperwork (writing the advertisements, inquiries, collecting applications) for our two undergraduate positions for this summer, and I also just got asked to move from my office shared with a technician into an office with two graduate students. I never complain and always find time.
I also don't ask my PI for much advice. I like to only talk research with him. When it comes to important career moves, I like to do my own research first and come to him only once I have narrowed down the choices. When I need real advice, I talk to other postdocs or other faculty who do not work with my boss. I only show my best side to my PI because I know he's the one who's going to write my letter of recommendation.
Just my 2 cents.