You can use whatever strength value for the environment that works for you, so if 20 is too dark, you can use 200, if 200 is too dark, you can use 2000, so if there is not enough of light, just add more light.
One thing to keep in mind is that if you have glass windows, whatever light comes through them, becomes refractive caustics, and they are terribly ...
I would try the real camera addon. It is free and gives you much more control over the camera settings. With it, you can change the exposure and other settings just like a real camera
Here is a link for it:
Resolution of HDRi doesn't change strength of light too much.
Resolution have an influence on sharpness of shadows.
Probably not visible too much between 2K / 8K, but for lightning with 256px result visibly differs (see end of cube shadow). Small sharp point as light source (like sun) produce sharp shade, in small images it can be just a pixel, but usually ...
In general - Render Properties - Film - Transparent works (viewport and render)
To Save render with transparency - Render Properties - Output - File Format - PNG and Color - RGBA has to be set (or any other format that supports alpha channel).
For viewport you can hide background image in Shading properties by ...
I don't think you can use an image like that as an HDRI, however, you can convert it into an equi-rectangular map that can be used.
Give a basic cube your Cube-map texture (it's default UV is already in the right shape), and align it properly in the UV editing tab. Make sure to connect the image through an emission shader (so it becomes it's own light).
Here, try this setup. I'm posting pictures of the same setup in both EEVEE and Cycles so you can see that the shadow is in the same place, just much more pronounced in eevee.
Here is EEVEE:
Now the same thing in Cycles:
You can see the shadow is there, just a bit muted. I could have played with the settings a bit more. I had to up the brightness of the ...
To append an HDRi texture from another blend file along with the nodes :
append the world
select the world settings from the properties panel
Click on the browse world settings to be linked
In that you will see the appended world with the name World.001 if it's not named and will appear with the name if it's named in the appended .blend file
The world will ...