I have a question when it comes to the shi’i belief of seeking intercession by the dead.

I have looked into the arguments and I fail to be able to rationalize invoking anyone other than Allah.

Firstly, there is no CLEAR authentic report where the Prophet or Imams taught us to make dua the likes of dua tawasul.

Do the shia believe that the Imams can hear us? What is the (authentic) proof for this?

Also in the sermon Imam Ali gives about the best ways of tawasul, invoking the Ahlulbayt is not mentioned at all.

Holy Quran 5:35
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O you who have believed, fear Allah and seek the means to Him and strive in His cause that you may succeed.

Holy Quran 17:57
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Those whom they invoke seek means of access to their Lord, [striving as to] which of them would be nearest, and they hope for His mercy and fear His punishment. Indeed, the punishment of your Lord is ever feared.

Holy Quran 4:64
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And We did not send any messenger except to be obeyed by permission of Allah. And if, when they wronged themselves, they had come to you, [O Muhammad], and asked forgiveness of Allah and the Messenger had asked forgiveness for them, they would have found Allah Accepting of repentance and Merciful.
Shirt was the cause of cure
Holy Quran 12:93
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Take this, my shirt, and cast it over the face of my father; he will become seeing. And bring me your family, all together."

A person never dies only the body dies but the spirit lives we have so many narrations that the dead people hear us and the verses of quran clearly indicates that the spirit lives and communicates especially the martyrs
Holy Quran 3:169
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And never think of those who have been killed in the cause of Allah as dead. Rather, they are alive with their Lord, receiving provision,
Holy Quran 23:99
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[For such is the state of the disbelievers], until, when death comes to one of them, he says, "My Lord, send me back
Holy Quran 23:100
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That I might do righteousness in that which I left behind." No! It is only a word he is saying; and behind them is a barrier until the Day they are resurrected.

There are more any many. But this is just a small token of abundant evidences that no intellectual islamic scholar could deny it.