Is buying pigeons from the market forbidden if it is probable that the seller acquired them via Facebook?

The general rule is that buying and selling are permissible. There is no obligation to investigate how the seller acquired the goods, as that falls under blameworthy excessive scrupulosity (waswasah). Even if it is known with certainty that the seller obtained the goods in a way that violates the website's terms and conditions, this does not prohibit buying them from him, because violating the website's terms does not render the goods themselves unlawful.