Is what I am doing – collecting the mobile numbers of members of a website for selling livestock and bidding on it, forming a team to sell them, and taking a commission on every sale made through me – considered Haram, especially since I took the numbers from the website without any conditions prohibiting it?

It appears there is no harm in you offering the numbers of those interested in bidding, and benefiting from what you are given if a deal is concluded through you, provided that the prevailing custom dictates your entitlement to a commission for it. There is also no harm in collecting numbers from available websites, as long as it is permissible to do so. However, if taking the buyer's or seller's contact information from a website requires the website owner to share with a second broker, then this falls under the ruling of multiple brokers working together.