Can HomePod mini connect to Philips hue hub and ring alarm devices?

Your HomePod uses siri to interact and because the home app supports siri and philips hue you can use your homepod to interact with your hue devices. But this only works when you add hue to apple home. This should normally work pretty easy.

the homepod just act the role of homekit hub you set it up on the home app on your ios device or mac

I added my hue hub to homekit, same with my Ikea trådløs hub that controls the Ikea bulbs