I'm interested in Gaussian blur layer that blurring all inside of some figure located on this layer.
I mean, blurred background of some exact area. And in case of I move this area, blurred image must be updated. If I move some object in background - blur must be updated. etc.
It sounds like you want to use an opacity mask (accessed through the Transparency panel).
This will apply the Gaussian blur to the interior of the object. If you move the masked art, the masking object will move along with it.
Here's an Adobe video that explains and demonstrates how to use opacity masks. https://helpx.adobe.com/illustrator/how-to/illustrator-opacity-masks-transparency.html
You can apply any effect on a layer and it will affect all items in that layer as if they were one item. Doing this requires you to know a non-obvious thing about the layer panel. That is that things are selected with the round ball next to the object name (and if its filled its applying an effect)
Image 1: Select the layer from round ball next to it.
Once you click on the sphere you can apply a effect, change strokes or do pathfinder effects on the layer contents. Because effects are live whatever you do on the layer below it will update.
Image 2: Layer selected.
Its worth noting that blurring is a potentially slow operation. So dont be surprised if the 300 dpi a4 size image takes a while to update. Tip: You can lower raster settings or disable the effect while you work with the data.
Image 3: Layer with blur applied to it.
PS: Please note that there is a huge difference in result form blurring each shape and blurring a layer.