Don't worry about the federal amended return. If TurboTax let you e-file it and the IRS accepted it, you're golden.
As far as attachments to your state amended return, you're correct that you do need to attach a copy of your federal Form 1040-X and proof of its acceptance. Since there was no overpayment or balance due, you don't need to attach any more federal items.
As far as Illinois documents, the instructions are fairly vague. According to What must I attach to my Form IL-1040-X? in the Instructions for Form IL-1040-X, you need to:
[S]ee the instructions for Form IL-1040 and any schedules to see what to attach.
Note: If the change you are making requires a supporting schedule or form, you must attach it to your Form IL-1040-X. Without proper attachments, we may partially or totally deny your claim.
According to the Instructions for Form IL-1040, you'll need to attach Schedule IL-WIT and your Forms W-2 and 1099 that show Illinois income and withholding. You should also "include any required attachments (e.g., Schedule M, Schedule ICR, Schedule IL-E/EIC, Schedule CR, federal Form 1040 and Schedules) with your Form IL-1040."
That said, considering the vagueness of the instructions, it won't hurt if you print and mail the whole amended return, excluding extension forms and any worksheets populated.
