The line in the photo is a result of using the digital camera. Each photo you take will show the line in a different position.
Your VCR should work without using the seperate modulator. If you have a VCR with 300 ohm outputs, that really is old!! Next time you're at Walmart, pick up a 300/75 ohm transformer to leave on the back of your set. Radio Shack will have them as well.
If that tube hums when you put your hand near it, stop putting your hand near it!
Nah, I don't think I've heard of that happening. Perhaps someone else has. The high pitch ring you hear is normal. If you were to play with the horz hold, you'll hear the pitch change as you are changing the frequency in which the tube operates. Some sets are pretty loud... others are not. My 72 Zenith is quite anoying I think.
The screw you mention... is it on the back side of the yoke assembly? If it's not for centering, it may be your focus. I think my Philco uses a focus like that. If you have your Sams for the set, the last page showing the rear of the set should tell you what that screw is for.
You got light on the screen and no nasty surprises... that's good! You'll find that you'll be doing lots of tweaking for a while once you run a tape or DVD for producing a picture. Keep in mind that if you run a tape in the VCR, the top part of the screen will likely pull to one side. That's pretty normal on old sets mixed with VCR tapes.
Also, you can plug a DVD player into the back of the vcr and set vcr to line in to get a dvd to play on it. YOur vcr would be working as your modulator for you.