If someone comes to the US with F-2 visa status, can he establish a new company in Canada or Germany and manages the company and gets it's incomes during the time he is inside the US with the F-2 visa status?
A can-I-work question was asked of Sylvia Gwin, an immigration attorney in Olympia Washington. She responded:
No work at all: no part-time work, or internship whether full-time or part-time is allowed for F-2 visa holders. F-2 family members may not work and may not attend school (except child under certain conditions).
Several lawyers (in the comments to that answer) indicated they agreed.
The conditions of an F2 visa prohibit "work," not just "work within the United States" or "work for a U.S. employer." Thus, the answer to your question is "No."
Working carries a worse calculus than your previous idea of starting-a-nonprofit: if USCIS discovers that you're working, they will not like it. You can guess the results.