I tried to reproduce your issue about OBJ export, but didn't notice problems on the DAE file I tried (but I didn't try 10 times).

7. Extract folder 01 content(3dmodel.obj/somthing) where Untitled_Export.obj saved

Even if it's not forbidden, you're not supposed to do that. Who would you do that? [;)]

10. Exported Obj is bigger and different, but mtl file is almost same.

Files are different but it's not astonishing, their coordinates are not in the same space:
- Imported 3D models and their counterpart in the .sh3d file are generally centered and often expressed in an other unit that the centimeter.
- Exported OBJ files use the same coordinate system as Sweet Home 3D, i.e. in centimeter and probably not centered on (0,0) point depending on where you placed your objects on the plan.
This leads to bigger values in Exported OBJ files and bigger files. Don't forget also to select the option Export selection option while exporting.

The door called 'OpenDoor' in furniture library when attaching to a wall (thickness of 24) is render like a stretched door panel.
By running through furniture.jar DefaultFurnitureCatalog.properties I saw its wall thickness is 7.5. I think it can be solved creating one more copy and rename like 'DoorOpened2'and also changing its doorOrWindowWallThickness#20 = 24 for those users are new in SH3D & complaining it.

I had the same idea for a long time, but don't like to put workarounds in the program itself. Adapting opened door to wall thickness is a complicated feature to program, but it will come one day. By the way, there are all kind of wall thickness around, and this would still be a very approximative workaround in many cases.

1. I am talking about both "Ni" and "d". I think transparency value (Ni/optical density) may not be defined correctly also transparency color is not defined in .Obj format like in .dae does.

I don't see any issue about the d transparency value in MTL files. The management of Ni index of refraction should be ok now. As Ni = 1 value in non sense, I wonder if I should rather choose glass index (1.55) rather than water index (1.33) in that case.

2. 3d window failed to refresh when it loose focusing […]

It's an old issue that happens for some users under Java 7 and still under Java 8. [:(]
That's the main reason why Sweet Home 3D installer is still bundled with Java 6u45.
With Java 7, I noticed it happens one time out of two mouse moves when you resize the 3D view.

3. When I apply a texture to sky it does not render in Arial view.

It's on purpose, as explained in the help about photo creation. I feel it gives nicer shadows. If you want your sky image, choose the same point of view in Virtual visit mode.

4. If you add a key combination like […]

I don't understand the goal of these keys. Keep in mind that Tab and shift + Tab are used to transfer focus, and alt + Tab to switch between applications under Windows and Linux.