going from iPhone 8 to 12 mini.

Hi,
Pressing the side button will cause your phone to lock. Pressing and holding it will activate siri.
In order to go home, you must swipe up from the bottom of the home screen until you hear two tones. Hearing a third tone means you'll activate the app switcher.
I wouldn't recommend the 12 Mini at this point. I would encourage you to go for the 14 as it's more recent and has a better battery. It's the smallest of the lineup, as well. Regardless, I hope you're happy with what you get.
Hope this helps.

Firstly, if you don't set up face recognition, you can still use your passcode to log in. Secondly, no, the side button isn't what takes you out of apps and to your home screen. That honor is given to a swipe gesture that could be a bit of a learning curve at first, but you'll get used to it. The side button does, however, activate siri, if you hold it down. All in all, the 12 Mini is a good little phone. I made the exact same transition back in January, so can definitely give you pointers.

It's also a question of price though. If it's a choice between paying through the nose for a 14 and not paying as much for a 12 Mini, I'd personally suggest that they get the 12 Mini. I only got the one I've got thanks to a friend giving it to me because they weren't using it any more and had upgraded to a newer model. Otherwise, I'd still be stuck with a 6 Plus.

I have moved from iPhone 7 to 12 mini and in between I used iPhone SE 2nd generation. You will need to get used to face ID and lackof home button but once you get it, you will never return to he model with home button and touch ID. I would recomend purchasing iPhone 13 mini it looks more or less as 12 mini but has better processor and battery lasts longer than on 12 mini. Wish you good