Why I can't open my project?

Why when I try to open project using button “Open Other” I can’t see files, which i need?

So I have to open some other project, in that choose File → Open Scene, choose scene from project, which I need and only then my project will be opened.

Maybe there is a better way?

And what the difference between files FPS.sln and FPS-csharp.sln?

The SLN files are solution files for Visual Studio and Monodevelop. Unity ascertains the project by the assets folder, project settings folder and doesn’t have a file type to open when opening the project. You open based off folder location. Like the one you’re in.

Because the solution file(s) can either be csharp projects(the assembly that builds out with the c# classes) or the java/unityscript mixed with csharp, they have created multiple files detailing the projects for csharp and unityscript and will link to corresponding .csproj(csharp) and .unityproj(java/unityscript) inside the solution file.

I think that you need to open a “Project” first then inside you can create or open a scene

When you’re in the folder just click open and the project should open fine