Try setting initialDir to content://com.android.externalstorage.documents/document/primary%3AMyFolder%2F
When you choose a dir with SAF Picker you will find tree in place of document.
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By clicking on it. (How else?) 
How can I get the selected file uristring ? With OpenDocumentTree block I get the uristring of selected folder, not the uristring of selected file-
I know the folder, I know the filename , is it possible to open it with only one pick ?
It is possible and a work of adding just one line. Its implementation will take few days.
OK, thank you, I realized that using OpenDocumentTree block and clicking as attached you can view the file content.
Can you explain me the difference betwen type and extraMimeTypes ? can I use them for showing my desired file only ?
I mean all filenames starting with P
Then you have to list all files first and check then which of them start with "P".
I need to pick file or folder for opening, after picking I get automatically write/read permissions, why there are permission blocks ? When I need to use them ?
Firstly, why is the file in the Download folder? Does it have to be downloaded from the cloud? If so, you can download it directly to the App's ASD folder:
However, Download is an Android shared folder, you do not need SAF to access it.