Right, the Hope uses up one of your four years of eligibility for the AOTC. (Note that the maximum credit is $2500, not $2000.)
You may need receipts if the IRS asks for them. Ultimately I suppose they would decide if the materials were “needed” or not. I don’t think they would see that level of expenses on pens and paper as “needed.”
The IRS does not generally take kindly to people playing games with their taxes, so I would recommend keeping it legit.
(Our daughters’ tuition is a lot more than $4K, so we’ve never had to worry about it.)