In response to your first question: I think the putt meter lacks the perspective lines because it's a slower meter and is made to be difficult. After all, putting on world class greens should be.
As regards your second issue: That space is shrinking because you have pulled back on the swing meter but waited too long to let it go. It's basically there so that you don't have all day to think about the proportion of power that you need for the shot. It just keeps you on your toes and forces you to make your decision quickly. It is a bad thing, since it narrows the margain of error by a great deal.
The diagram you drew, something like this: | | | | |
The center line, is of course a perfect shot. The small range that surrounds the center line is basically the safe zone. If you keep your shots between those parameters, your shots won't stray too far from your target line. When you start to miss shots outside of those lines, you'll pay for it with sprayed shots.
Hope this helps,
-Dylan