Apparently, from what I've heard today, he wouldn't necessarily be able to see the plane from the tower. And I don't think a visual check is required before take off. Not with one person in the tower, probably performing more than one task, none of which would take him/her near a window.
Provided the runway ends are visible from the tower, I personally would get a visual confirmation that everything appears OK with my departing aircraft. I can't judge this controllers actions, though, with limited information.
Really? I have never heard such a thing. I always thought that was a part of ATC. In fact, I could not qualify for ATC in the USAF, due to my vision - needed 20/20 uncorrected.