1. You can look around the web for Lua tutorials. If you have any programming language knowledge, it's pretty easy to learn.
2. Notepad++/Sublime Text or any text editor actually. There isn't really any IDE for a such language.
3. Easy for small and simple projects, but it depends on the framework and complexity of the project.
You can get Mari0's source code by getting the .love file, renaming it into a .zip file, and then unzipping it. You should see a ton of .lua files and folders, and they are all editable. Once you finished a change, zip the files back into a .love file, and run it.
Mari0 uses a Lua engine called LOVE2D, and so you should check its documentation on the website.