Does Blender run on Linux?

Blender's download page lists Windows, macOS and Linux side by side at the same version, currently the 5.2 long term support release. For Linux you can take the compressed archive from Blender directly, install it from the Snap Store, or use the Flathub listing under the id org.blender.Blender, which is the easiest route because your app store then handles updates.

Your files come over exactly as they are. A .blend file is the same file on either system, and so are the add-ons, which are written in Python. Where care is needed is in the paths inside a project. Textures and linked files referenced by a Windows drive letter will show up missing on Linux until you point the project at their new home, so use relative paths or repack your textures before you move.

Linux is not an afterthought here. The Linux build is released at the same time as the Windows one and the program looks and behaves the same. If you render with your graphics card rather than your processor, check that your distribution has installed the manufacturer's graphics driver, because that is what the acceleration depends on.