The size and placement of the brand logo is determined based on the information you want to convey.
When the mark is larger, it takes on the most prominent role in the piece. When the mark is smaller, it becomes secondary information that recedes into the background. Placing the mark in the top or right side of the piece also adds prominence because users typically read from the top left to the bottom right.
The brand logo should not be paired with other marks because a secondary mark has already been incorporated into the logo.