What are some software that will use this resource as features?
Like simulating a crash or earthquake effect.
The RPG game Silver Snail use this when the player receive a hit.
If someone manage to delete this statement from the MSX-BASIC list, it will work on MSX1 computers too.

Scrolling.
Is this true that Space Manbow use this on MSX2?

Some software use this for adjusting the screen on games.
Examples:
Zanac Ex
MSX-FAN Disks
"Daikoukai Jidai"

Is there any demonstration program that use this?

Yukio: set adjust (R#18, I believe) is used in SD Snatcher, amongst others. Space Manbow uses it excessively, to simulate a smooth scroll. VScreen does that as well, as does Manbow2. Nothing new there.
It would never work on MSX1, because MSX1 doesn't have an adjustment register.
Scrolling: Space Manbow uses the adjustment register to scroll and does some HMMMs and the backdrop to simulate a smooth scroll. Of course, for vertical scrolls, it uses the vertical scroll register, R23.

Other than that, I'm pretty clueless as to what you're trying to point out here.

...and some games like SD-Snatcher or Garyuo King do not leave unmodified the adjustment setting after the shocking effects. This is pretty annoying as I have to use set adjust to center the image in my TV. After the first shock effect, the image is not centered until I return to BASIC and adjust again.

I believe Usas and Mr.Ghost use "Set Adjust" effect as well.

In SD-Snatcher it's only used in the battle screen (when ya get hit)
The main scroll in the game is just 8x8 tiles movement.

Also lotsa demos use the "set adjust" feature, mostly for scrolling big contents (big fonts for example).

It's a widely used trick. Why are you so interested in that?

SET ADJUST = Move screen + save to sram

R18 = Move Screen


That's the difference.