Is it an installation or a ship? Couldn’t it move around the galaxy to attack different planets? If so, I think it’s more of a ship than a base. Only analog I can think of in our world would be aircraft carriers or battleships, which are commonly referred to as floating cities, yet they don’t have children or spouses living on board.
I don’t think so. The Death Star was a military vessel, and spouses/children don’t usually don’t get to come along on those sorts of things. Having said that, maybe there would be some children on if there was some sort of christening celebration or school field trip on board at the time of the attack.
It’s really a fun joke, but since I usually just assume most people are terrible, if I saw this sticker, I’d immediately conclude it was placed by some entitled parent that felt like this public pole belonged to them. And if someone made this sticker of my son’s bike, I’d be afraid it would attract a troll who would purposefully lock their bike on top of it or otherwise fuck with the bike simply because of the picture.