EAD & H1B - 移民

I'm using my H1B to work for my currently company.

One month back, I received my EAD/AP because my husband's company applied
greencard for him.

Do I need to inform my current company that I have EAD/AP and ask them
to change my immigration status in the company's system?

I'm asking this quesiton is because I want to start doing my own business
(as a part-time job) and I heard that if I am using my H1B working for my
current company, I can take another job using my EAD but I can't
receive any income. Is that correct?

Thanks!

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