When it comes to saving, I found that this is currently not supported, see https://github.com/microsoft/azuredatastudio/issues/20219 Bear in mind that the current version is 0.1.1, a number that suggests that it is far from feature complete.
As for analysing slow queries that is a wide topic and a Profiler like this is just a tool. As long as you are only running queries in Azure Data Studio, you don't really need it, since you can wrap the queries in SELECT sysdatettime()
to measure the execution time.
But say that you are running an application, and you want to know that takes time. Then you can set up SQL Profiler, filter for that application and see what calls it are making.
If you are running a stored procedure, you may want to see the individual statements inside in the procedure. There are events to capture this, but SQL Profiler in ADS does not yet seem to support them. There are other Profiler tools you can use for this purpose. Before I start to suggest too much: are you on Windows or are you on some other platform?