I don't know if PayPal would let you change the ownership of the account. You have to ask PayPal about that. Even if they do allow it, any payments that you received prior to the change still went to you personally, not to the club.
If the club sets up its own PayPal account, and the donations are made to that account, that would get you out of the loop and eliminate your tax problems. But again, that would only work for future donations. The payments that were already made to you are income to you.
The organization only needs one determination letter. The determination letter is for the organization, not for a specific activity or purpose.
You seem to be mixing up reporting prizes and reporting donations received. The Notice 1340 that you quoted is about reporting prizes. For any prize of the specified amounts, the organization has to file a Form W-2G with the IRS and give a copy of the W-2G to the person who won the prize. I don't think the organization has to report individual donations, regardless of the amount, but check with a tax professional who specializes in non-profits.
