Is it permissible for a new merchant in the same field as another merchant, who has many followers, to follow the accounts of the first merchant's followers and offer them his goods, or to reply in the first merchant's account, advertising his goods, with the aim of acquiring customers, and is this considered as "selling over the sale of his brother"?

Announcing a commodity and making it known to people is not considered a sale over a sale or a bid over a bid. Rather, it is prohibited only if it occurs after the price has been settled and the buyer has committed to the seller.

Promoting a product to a merchant's customers and offering it to them is permissible, unless it involves a violation of their privacy or an الاطلاع (accessing/viewing) of what they dislike being seen without their permission.