A: It is not a good idea to work with this client. You don't indicate whether the client was someone that you worked with (taught) in the past for her. However, a non-compete means you cannot solicit or work with her clients while employed by or while you have an independent contractor agreement and non-compete with her. Typically these contracts are enforceable for a duration of time and within a certain radius of her establishment (this depends on the state, but 2 years and 50 miles is typically a baseline). You don't want to draw a lawsuit or lost future business over one client. Financially, its not worth it.
A: The statute you quoted is incomplete. It should read 735 ILCS 5/ ___ and a number after the slash in order to point to a relevant section of the statute that your landlord is reading. At any rate, you are not required to give thirty days notice unless it specifically states so in your lease. Assuming you have no contract with your landlord and no specific clause in the lease regarding the amount of notice you must give, you do not have to stay and pay march rent. Sounds like he/she does not have a renter yet. You may want to have an attorney review your lease and send him a letter for a minimum fee.
A: Well, its your lucky day. The amount of check from the insurance was based upon an estimate of damage provided to them by their adjuster or an outside body shop. The fact that the body shop charged you less in the end should not change the amount of the check from the insurance. If the check is made out to the body shop and not you, you can ask the body shop to reimburse you for the remaining $2,500, but I strongly recommend you have them place in writing that they owe you a refund of $2,500 before you give them the check. Make sure you tell the body shop you have a large deductible --they don't need to know the amount. If you have any questions, feel free to contact an attorney to follow up.