How could I access multiple databases at once using Azure Data Studio and import an existing .mdf file as one of those database, with tables and data that had been stored in that .mdf file?
Azure Data Studio is like SQL Server Management Studio: these are client programs that access SQL Server, but ADS and SSMS don't touch the MDF files directly.
What you need is SQL Server to open the MDF. Try downloading SQL Server Developer Edition - it's free. Once it's installed, follow the instructions on how to attach a database. Attaching a database is kinda like opening a .doc file in Word - you need Word installed first.