The Mono project focuses on compilers and runtime libraries and does not directly provide an IDE. Developers must choose from a series of available tools the one best suited for them.
MonoDevelop is a Mono/C# Integrated Development Environment for Windows, Linux and macOS. It parses your C# and VB programs as you type them and is able to provide contextual completion of methods.
In late 2003, a few developers from the Mono community began migrating SharpDevelop, a successful .NET open source IDE from System.Windows.Forms on Windows to Gtk# on Linux. A rebranded version named Xamarin Studio is sold by the commercial sponsor behind the project with proprietary iOS/Android addins.
As you might expect, there are many development tools available to C# developers, ranging from bare-bones text editors to complex integrated development environments.
Using Emacs or Vim
Emacs and Vim are general purpose text editors, not IDEs designed for use with .NET and C#. However, you can use them to write software in nearly any language.
For Emacs, you will want to use the C# major mode available at www.cybercom.net to handle syntax coloring and proper indentation. You may want to install the OmniSharp plugin for autocompletion and various other features.
Vim supports syntax highlighting for C#. For autocompletion, the OmniSharp plugin is also available.
The Eclipse IDE can be used to edit C# code, but lacks completion of methods. The emonic project is not maintained anymore.