Apologize if I place this question in the wrong topic.
I make a drawing. To make it easy, I make some layers. One of the layer I named Measurement Layer. As indicated by the name, I intended to make all measurements in that layer, and it works. Unfortunately, the layer become like layer 0, which mean, everything I draw will be put in that layer, and I have to move it to main layer (layer 0). If not, if I put invisible that Measurement Layer, the new entities I drew also invisible. I have check if any setting regarding this problem. Unfortunately I couldn't find. So please, please help me. This is annoying.
I think that you simply didn't activate the right layer.
There is always one active layer where new entities are drawn. When your newly drawn entities are placed on the 'Measurement' layer, this is the active layer.
Your screen shot is very low resolution, but I think I can see that the Measurement layer row is a little bit darker there.
To place new entities on layer 0, first click on the layer 0 name in the layer list and then draw. This should do the trick.
On Windows there is an issue with desktop themes. In the standard theme, selected rows in list views, like the layer list, are highlighted with a very very light grey or blue. Thus it's sometimes hard to detect, which row is selected. And the selected row marks the active layer.
Take care when switching the active layer. There is a feature in application preferences (Defaults), where you can modify the layer of selected entities when switching the layer. That means, when you have entities selected and activate another layer, all selected entities are moved to the new selected layer. This can be very useful, when you're aware of it. But if you don't know about this feature it could be annoying.
What is that mean "to activate?" If the meaning to put it visible/invisible (by clicking the eye), of course I do. Of course I activate the layer 0. In the contrary I put invisible the Measurement Layer as I don't to see all the measurement as I makes too crowded. I have try to search if any setting I missed, included to check the lock and the hatch icon. But both are not related to the problem.
To activate a layer means to click on its name, not the icons in the left columns.
Toggling visibility or printing doesn't activate a layer, this is by design.
As I wrote before, on your screen shot is visible, that the Measurement layer row in the layer list has a light gray background. When you click on the layer names, this should change. The light gray background marks the active layer.