Yes, the donor of an item he or she created is entitled to a deduction, but in many cases, the amount of the deduction won't be fair market value. Artists are generally limited to cost basis for contributions of property they create and donate to charity. And unless the recipient 501(c)(3) church/charity uses the property in its exempt activities, donors in general are limited to cost basis deductions (not fair market value) for contributions of appreciated tangible personal property (items other than securities, which are intangible, and land and buildings, which are real property). Selling something that is given to the church/charity is not considered using it in the organization's exempt activities.
And yes, the bidders/buyers may be entitled to a deduction for a purchase if they pay more than fair market value for it, and they do so knowingly and intentionally. A church can help its bidders/buyers document their intent to make a contribution by giving them information in advance about the estimated fair market value of the items up for auction.
As is always the case, you have to be careful to make sure the acknowledgments (receipts) you issue for such activities are appropriate under the circumstances. Special requirements apply to receipts for contributions for which the donor received something of value in exchange. IRS Publication 526 is a good source of information about such requirements.