You’re doing well – just one thing you need to change, and I reckon it’s a totally reasonable mistake to make:
This:
add_action('wp_enqueue_styles', 'alpha_styles');
needs to become
add_action('wp_enqueue_scripts', 'alpha_styles');
Why scripts? Because there is no WordPress action called wp_enqueue_styles. Although the functions are named wp_register_style & wp_enqueue_style, you still need to hook them to the multi-purpose wp_enqueue_scripts action.
Yes, WP core should probably just add a second action to save this issue from occuring… 🙂
Although it can be a pain at first, once you get your head around how the enqueues work, it’ll save you a lot of time in future. There’s several benefits: dependencies can be managed easily; your scripts & styles will function across multiple headers and footers if you have them; and plugins that hook into scripts & styles (eg. to concatenate/minify them) can do their job.