Yes, the MS SQL Server Express edition is free for use, also for commercial purpose.
See Microsoft® SQL Server® Express License Terms for Redistribution and Hosting
Keep the limitation for the edition in mind.
This browser is no longer supported.
Upgrade to Microsoft Edge to take advantage of the latest features, security updates, and technical support.
What free SQL Server editions am i allowed to use in a production environment (for commercial use) in Windows where i both use .NET web-applicationa as well as desktop applications?
I have investigated some of this but it's not clear - i do know that i am not allowed to use SQL Server Web Edition for my desktop applications (but apparently SSMS is allowed).
Is SQL Server express an option ? Are there any limitations to this ?
Yes, the MS SQL Server Express edition is free for use, also for commercial purpose.
See Microsoft® SQL Server® Express License Terms for Redistribution and Hosting
Keep the limitation for the edition in mind.