Does doubt about the intention behind the marriage代理 (tawkil) or the father not hearing it affect the validity of the marriage contract (aqd al-qiran) that was based on this proxy? And is it a condition for the father to say, "I have accepted the proxy"?

What you have done is sufficient for the validity of the power of attorney. Indeed, a power of attorney is valid with less than that, whether it be a statement or an action that indicates it. Your doubt about the validity of the power of attorney and your question about the validity of the contract are unfounded, and this is evidence of the firm grip of whispers (waswas) on you. So, seek Allah's help and do not falter, and turn away from these whispers and pay no attention to them.