This would prove that a very powerful intelligence exists.

It would not, by itself, determine the character of such a being or the legitimacy of whatever claims it would make upon me or humankind.

Indeed, my first impulse, based on the principle that absolute power corrupts absolutely, would be to not be noticed by such a being if possible, much less trust it.

Proving the existence of a god would only be the first step on a very long road to trusting and certainly to worshiping such a being. Also, the communication would have to be a two way street. After all these thousands of years, all these wars, all these tragedies ... surely some pointed questions should be asked, and answered with candor.

Eh. I suppose I'd scour the news for Police Box sightings for, like, a few minutes until it stopped being funny and then I'd assume it's some kind of tech someone's been working on in secret. Or that I'm hallucinating, as happens to narcoleptics.

The atheist, William Rowe (late head of Philosophy at Purdue), claimed that such would count as empirical evidence for the existence of God although it would not be conclusive. He used this example (where it was a voice everyone heard in their own language) in the attempt to refute the claim that in principle there could be no empirical evidence that would support either theism or atheism--and, hence, the entire question is meaningless. So, for him, it is a meaningful issue and since in practice no such empirical evidence ever occurs (and also for other reasons), he was convinced atheism is true.

Perhaps - would depend on the exact circumstances as it could be very advanced ET. It might slightly stronger evidence if the blind would indeed see (have their sight restored, eyes regenerated if none existed.)

When I've been asked what it would take for me to consider evidence for the existence of god, I have replied when artificial limbs are left behind at Lourdes instead of crutches. The rapid, spontaneous regeneration of a limb would certainly be evidence of an extremely advanced technology (where does all that mass come from that creates the new limb) or a supernatural power.

Blind people seeing and understanding in their minds eye might make you wonder - but I would suspect some sort of advanced technology would be more believable than what people generally imagine to be "god". I would expect god to talk to my heart, not communicate through general propaganda.