Will home pod mini connect with Samsung TV?

Only with (at least) second gen Apple TV Box with the HDMI cable plugged directly into the ARC port on the tv. The tv would need to have this port. This will allow all audio on the tv and Gaming Consoles etc to go to external speakers such as HomePods and the HomePods should be set to default Audio in the Apple TV settings.

Use HDMI ARC or eARC with your Apple TV 4K - Apple Support

Set up home theater audio with HomePod or HomePod mini and Apple TV 4K - Apple Support

If your tv does not have this ARC port you can still use any model Apple TV to play to HomePods but only for watching on the Apple TV Box

most likely not

the homepods support airplay 2 as means of being used as speakers, this is only really supported by ios devices macos devices and windows computers using itunes, and appletv boxes

even tvs that support airplay 2 support it as receivers not as transmitters