With name spacing, you need to tell your composer.json what your namespaces are and where the code sits - once you have that, you only need to composer dump-autoload once.

Once you crack that, points 2, 3 and 4 will be fixed.

For example, in your composer.json you need to add a psr-4 reference that states what your top level name space is, and then where that code actually sits.

Say you have a name space called MyNameSpace and you put your classes in /app/MyNameSpace/ folder, it would look like this:

	"autoload": {
		"classmap": [
		...
		],
        "psr-4": {
                "MyNameSpace\\": "app\MyNameSpace"
            }
	},

Add that, run composer dump-autoload and now Composer knows where to look and then Laravel's autoloader will, in turn, know where to to look.

Jeffery Way did a good primer on it on Laracasts, and it's freely available: https://laracasts.com/lessons/psr-4-autoloading

If that wasn't clear enough, Phil Sturgeon did one too: http://philsturgeon.co.uk/blog/2014/01/autoloading-laravel-application-code-with-psr4