There are no forms for what you are doing, because you're doing it all wrong. The donations should have been made directly to the dog club, not to you. Any money paid to you is not a tax deductible donation for the donor, even if you give the money to a charitable organization. The money that people paid to you is taxable income to you, and you will have to report it on your tax return.
PayPal is not a bank. (I don't think it would make any difference if it were a bank.) Yes, you will get a 1099 from PayPal. Having an EIN would not make any difference. If the EIN is in your name, any income reported to your EIN is still income to you, the same as income reported to your SSN. Having an EIN does not create a separate entity or organization, or relieve you from having to pay tax on the income.
Money paid for raffle tickets is never a tax deductible charitable contribution, no matter who the money is paid to.
Being a non-profit is not the same as being authorized to accept tax-deductible contributions. In order for contributions to the dog club to be deductible by the donors, the club has to get a determination letter from the IRS authorizing it to accept tax-deductible contributions.
