Now we have a problem with not shared ones. For not shared ones, we get name of the folder back but not the whole path. nameis valid but pathloweris null. Can we get a metadata for not shared folders? We tried below 2, but it did not work.
When you use the Chooser with the linkType: "preview" option, you'll always get back a shared link back in the "link" field, which can be used with /2/sharing/get_shared_link_metadata, whether or not the folder was previously shared.
Note that this doesn't work with the linkType: "direct" option, since that doesn't result in actual shared links. I notice that the options you indicated originally do have linkType: "direct", but I expect that was just a typo, since it's not possible to use the linkType: "preview" option with the folderselect: true option anyway.
Anyway, the /2/sharing/get_folder_metadata and /2/sharing/get_file_metadata endpoints are meant for different kinds of sharing (shared folders and shared files, respectively, not shared links), so they won't work with the shared links returned by the Chooser.
The /2/sharing/get_shared_link_metadata endpoint will only return the path_lower value if you are using an access token for the same account as the one that was used to select the folder in the Chooser. It sounds like that wasn't the case in some of your attempts, so the field wasn't populated.
Likewise, if you specify the file path or ID for a file from a different account when calling /2/files/get_metadata, it won't be found.