He's asking if she's heard anything that he's said, and he's probably asked her to reconsider the divorce/break-up.
"(Rather be lonely in love, than alive with you and dead)"
He's saying that out of the three choices, he'd rather deny that the divorce/break-up ever happened, as opposed to being alive and living in the real world or being dead.
"Have you ever heard a word?"
Same as above
"Hear me out this time (hear me out this time)"
He's saying that he's asked her to reconsider the divorce/break-up and he wants her to at least listen and hear him out.
My take on the chorus is this:
"Have you ever heard a word?"
"(Rather be lonely in love, than alive with you and dead)"
"Have you ever heard a word?"
"Hear me out this time (hear me out this time)"