1. Theoretically, you can work for as many companies as you like on EAD. My concern would be the implication that you no longer have a full time job with the sponsoring company, which is a requirement for the green card.
2. Since you are on a derivative EAD, you have even more freedom than the primary applicant. Other than an S corporation (I think that requires green card under tax laws), you can form any kind of corporation (LLC, etc.), but do check on the State law.