Visual Studio (VS)
For some students, VS Code simply does not work well. In that case, install and use Visual Studio (Community Edition). Maybe due to a problem with Unity, some update or whatever.
Download VS and follow this instruction. That should work.
If you still experience problems with IntelliSense, maybe you’ll have to download the MS Build Tools. For further information, please refer to this thread, which was linked by Carlos.
Regarding the namespaces, go to Edit > Preferences > External Tools (in Unity) and click “Regenerate project files”.
Sometimes, Unity has got internal problems. If nothing helped, close Unity and your script editor. Go to your project folder and delete the Library folder. If you see a Temp folder, delete it too. If you use Visual Studio, also delete the *.csproj and *.sln files. Start Unity again. Don’t panic if you see an empty scene. That’s Unity’s default scene. Open your own scene in the Assets folder. Now everything should be working.