First and foremost never play any games with a bankruptcy court. If it will not stand inspection with all the facts revealed do not under any circumstances do it. I see nothing wrong with starting a business. In terms of what you have to report and when please talk to your lawyer.
Sure you can start a business. And the income from it will be available to the trustee to pay your debts. Having someone else as your "front man" does not change the fact that it is income that the trustee controls. If you are talking about setting up a fraudulent arrangement to avoid paying your creditors, then you would be committing bankruptcy fraud, and could get free room and board at "club fed" for a while. You really need to play by the rules.
All of your disposable income must be devoted to your chapter 13 plan. If your income goes up, your plan payments have to go up too. Thus, chapter 13 as currently constituted creates a perverse incentive to sit on your hands insteaqd of maximizing your income. Bad policy IMO, but it's what we all have to live with.