My surprise would border on heart attack to find out that Rav Chaim Kanievsky knows that a computer even needs to be turned on let alone where the power button is. So I doubt e-mail is an option. But they all take letters as far as I know.
True story:
I had the letter I wanted to send to Rav Chaim in my pocket and I went out to get some envelopes and stamps. I fill out the address at the post office and put on the stamp, then put in my folded letter and give it to them. Walking home I reach into my pocket and pull out…the letter to Rav Chaim. So I go back and send it again. Two weeks later I get a response to my letter…and he returned my shopping list as well.