1. Your style needs to be set as a Quick Style to appear in the gallery. You can change the priority as shown in Suzanne's page.
2. You can also use the Styles Pane to view all of the styles, whether or not they are Quick styles. The Styles Pane by Suzanne Barnhill, MVP
3. You can attach a keyboard shortcut to a style.
4. I gave you a separate link about [Quick] Style Sets but because of the way this forum is formatted you may have missed it. Again: [Quick] Style Sets.
5. Here is a link to my free Add-In that gives access to more styles tools in the QAT: Styles QAT Add-In. It contains no macros and gives access to the Styles Drop-Down, the Styles Pane, and the Quick Styles Gallery under all tabs.