No screw fitting is required. Just need double-sided tape and it will fit on the wall. Also, it will stay on the wall for a long time.

Yes, any size tube will fit.

It comes with a sticker.

Yes

The strip is pretty big and of good quality. I don't think you would have any trouble mounting it to the tile.

Manually have to squeeze it down

It needs to hang or be up against the wall. You can have it mounted low but it is not free standing.