Is the marriage valid in which the guardian and the husband were represented by proxy by the elders of the family, and the husband did not verbally authorize his brother due to the prevailing custom?

This contract is valid—God willing—and is not invalidated by your not having verbally articulated the agency to your brother for accepting the marriage. Some scholars have explicitly stated the validity of agency without stipulating a specific صيغة (formulation) if its place is taken by custom or common practice.