There is no formal VS Code extension for Azure Data Explorer.
I assume that you are talking about the donjayamanne.kusto extension.
Please note that according to the extension changelog, it was last updated in September 2021.
Also, as can be seen in the changelog (and the GUI), this extension supports connection to Application Insight, however there is nothing mentioned about Log Analytics.
2.
Keeping the terminology straight will assist you to progress in the right direction.
You didn't import a few sample DEMO clusters, you connected to a single publicly available cluster, named help, a cluster that holds multiple databases.
https://learn.microsoft.com/en-us/azure/data-explorer/web-ui-samples-gallery
3.
A cluster URL is in the following form
https://<ClusterName>.<Region>.kusto.windows.net/
https://learn.microsoft.com/en-us/azure/data-explorer/troubleshoot-connect-cluster
https://learn.microsoft.com/en-us/azure/data-explorer/web-query-data#add-your-cluster
If you're using a free cluster, then you can see it's public URL at the same place where you have created it

If you're using a standard cluster, then once again, you can find its public URL at the same place where you have created it.

4.
I see no reason for you to run KQL queries in VS Code when you can use Kusto Web Explorer
https://dataexplorer.azure.com/
You can use it to query ADX clusters as well as Application Insights and Log Analytics workspaces.
https://learn.microsoft.com/en-us/azure/data-explorer/query-monitor-data