Usually no notice is required. There can be consequences, but none of them involve jail or anything. Quitting with no notice may get you put on a "never rehire" list at the company. Your reputation among your network may suffer and make future prospects more difficult. If you are receiving any company benefits that require a certain time of employment (education reimbursement, etc), you may owe some cash back for those. It should be detailed in your employee handbook or contract. If there's someone you trust to probe at HR with specific concerns, you can try that, but they are there to protect the company, not you, so tread carefully. Otherwise, find a lawyer

Depends on the state. Some states ban non-compete clauses entirely, some others have an income threshold, and some don't have any specific language either way.