Can F2 visa holder become a shareholder of one company? Is that legal if F2 visa holder has income from her shares?

Yes. It is perfectly legal for Aliens to invest in U.S. Corporations. Receiving income from the Corporation is also allowed, as long as it is in the form or Dividends and not, in any way,compensation for services rendered by the Alien.

You can do it, but be mindful that the corporation does not elect S Corp. taxation. For an S Corp., owners must be US Citizens or Lawful Permanent Residents. This response is general in nature and is not legal advice. The facts presented are too limited to provide a legal opinion. For a thorough legal opinion, you should consult an attorney.

You can invest and derive profits from a passive investment. You cannot participate in runnung the company or working.

Invest? Yes Take a share of the profits?????????? Maybe, it must be done very carefully. Personally, I don't recommend this risky path ... unless you're not planning on getting a greencard in the future.