Is it permissible for the one entrusted with distributing Zakat funds to take a portion of them for himself, given that he is in need of marriage, completing the construction of his home, and is burdened by debts?

The agent is not allowed to take anything from the money entrusted to him for distribution, because he is a trustee. He is not permitted to dispose of it except as authorized. If he does so, he must inform the owner of the money. If the owner approves, then all is well. If not, the agent is liable for restitution. Similarly, it is not permissible for a wealthy person to take Zakat. Nor is it permissible for him to take it to give to another without the owner's authorization, because this is a breach of trust.