You can't start and work for a U.S. business on a G4 visa; you can look into starting and operating a business out of your nation of origin.
A G4 visa is a non-immigrant visa, so once you have intent to immigrate you can no longer lawfully enter the U.S. on that visa. If you have taken steps to get immigrant status, the USCIS will be aware of your intent; if you enter and take actions suggesting that you misrepresented your intentions, it's possible that the USCIS will take action at some point - it will depend on the facts and what they are able to learn about your actions and intentions.
An immigration officer can consider the fact that you have applied for the DV Green Card Lottery when you enter the U.S., but of itself, registration would not ordinarily be sufficient cause for visa denial or refusal of entry.
He would need to discuss his employment situation with his employer.
Whether you work legally or illegally, if you earn taxable income you are required to pay taxes.

