Do plugins for Kerbal Space Program work on unix?

With very few exceptions, KSP mods are either parts only (and thus consist only of configuration files) or include plugins written in C# (which work on both Linux and Windows). MechJeb and Protractor specifically I can confidently say work on Linux because I'm using both right now.

All mods - parts or plugins - should be installed to the GameData directory. For example, if KSP were installed in ~/Games/KSP, with MechJeb installed you should have a directory structure that looks something like this:

~/Games/KSP/
  ...other KSP directories...
  GameData/
    Squad/
      ...base game files...
    MechJeb2/
      Parts/
        ...MJ part configurations...
      Plugins/
        ...MJ plugin DLL and PluginData files...

Bear in mind that with MechJeb you need to install a MechJeb part on your rocket to see any UI changes. Furthermore, if you're playing in career mode, you'll need to unlock it in the tech tree before it appears.

It depends on how the plugin was developed. Unfortunately, it's basically impossible to tell which IDE was used to compile the DLL. As far as I know, parts only mods should work regardless of the platform (although the wiki is somewhat vague).

As for where to put mods, each mod keeps all of its data in a single parent folder that's typically named after the mod. In this folder there will be at least a "Plugins" and/or "Parts" folder, with the possibility of a source folder as well. Note that some mods use plugins developed by others, such as the B9 pack, which uses the Firespitter plugin, among others. These plugins will generally be contained in their own parent folder to prevent loading two or more DLLs with the same name. All of these parent folders should be placed in the "GameData" folder.