Why is $provide only available in the ‘angular.mock.module’ function, and $q only available in the ‘angular.mock.inject’ function?

You can’t use $provide within the inject function because the former registers providers for the latter to use. Take a look:

describe('...', function() {
    beforeEach(function() {
        module(function($provide) {
            $provide.constant('someValue', 'foobar');
        });

        inject(function(someValue) {
            var value = someValue; // will be 'foobar';
        });
    });
});

You can though write your test this way:

describe('...', function() {
    var serviceMock;

    beforeEach(function() {
        serviceMock = {
           someMethod: function() { ... }
        };

        module(function($provide) {
            $provide.value('service', serviceMock);
        });

        inject(function(service) {
            ...                         
        });
    });
});

In fact, you don’t even need to implement the mocked service before injecting it with $provide:

beforeEach(function() {
    serviceMock = {};

    module(function($provide) {
        $provide.value('service', serviceMock);
    });

    inject(function(service) {
        ...                         
    });
});

it('tests something', function() {
    // Arrange
    serviceMock.someMethod = function() { ... }

    // Act
    // does something

    // Assert
    expect(...).toBe(...);
});

Here’s a Plunker script illustrating mostly of the above.