1. She can NOT do this on H-4. Once you folks file 485 and get EAD, things will be different.
You can then be a passive investor (performing no work type activity for the company) even while on H-1. You can also be an active investor if you wish to move to EAD as long as you maintain your intention to work full time for the GC sponsoring employer. Your wife can work for the company, own it, be partners, etc. as long as she has the EAD.
2. I think that should be fine. But passive means performing no work. Think of it as investing in IBM on the stock market. Just because you purchase a few shares, you do not get a seat at the Board of Directors of IBM. That is passive investing.