Information about the number of staff and board members (including the names of people on the board) of a nonprofit organization can be found via GuideStar. You need to register (free) on the site to see the IRS Forms 990 and other documentation that will be useful to you (there are also some fee-based levels of registration that will allow you to access yet more data).
As for the bylaws -- the Citizen Media Law Project has a page for "Bylaws for Nonprofit Corporations". They write:
"Nonprofit corporations are required to write and keep a record of their bylaws, but do not have to file them with a state office. Thus, unlike amendments to the articles of incorporation, bylaws may be changed without officially filing amendments.
"The incorporator(s) (i.e., person(s) filing the paperwork) or initial director(s) (if named in the articles of incorporation) generally have the authority to adopt a nonprofit corporation's original bylaws at the nonprofit corporation's organizational meeting."
The Foundation Center offers "Where can I find information on bylaws for nonprofit organizations?", though it does not explicitly cover how to hunt down existing bylaws of specific nonprofits (they give links to some real-life bylaws of a few nonprofits who have posted theirs to their websites). You may want to put your particular question to one of their offices or use their Online Librarian.
(I found the Citizen Media Law Project page via a general Web search; the Foundation Center and GuideStar are resources I was already familiar with and have used for both Rad Ref and personal research.)