For the installer, it would be a good idea to have it also package/install the version of .NET that your game targets (this can be found in your project's properties, if you don't know). Assuming you're targeting MonoGame for WindowsDX, it may also be worth your time to have your installer package/install DirectX. Up to you though, both of those will already be on pretty much any player's machine, but if it/they aren't your game will likely crash on startup and your end-user won't understand why.
As for hiding your content files, there are a number of ways, but most would require a decent amount of work. Namely, setting up your own content processor that extends/replaces MonoGame's default ContentManager. The simplest way, without any programming work, is to just make the files "hidden". Under default windows settings, they simply won't appear. Nothing else to it. However, you can go as far as embedding and even encrypting your content files into your executable. Research the options and their various pros/cons before committing a lot of time to anything. For example, with the embedding option, the files will be "hidden" within your executable, but unless you do anything else with it they'd be easily extractable via a simple .NET decompiler, and therefore probably wouldn't be worth the effort to make that work. Additionally, it makes your executable pretty large, and effects the way it's loaded and such.