Animals will approach cages on their own rarely, but if you put food they like inside it (with a stockpile), they will be attracted to them. As for their pathing and movement, they pick spots around the map (which they can reach) at random, so it's possible they could show up and just stick in one area, or they could zip across the map. It's best to litter the cages around the map to cover more area, but putting food inside the cage will help them move towards them.
It sounds like the water block you are designating on isn't accessible because it's probably at the bottom of a cliff. Entities can only climb up one block high, so make sure there is a path down to the water you're designating on. You might need to build a ladder or stairway down to the water.
I'll test this out this week and see if I can fix up some of that behaviour. Thank you so much for the detailed explanation. It seems they just get fixated on some other target way off, somehow missing the check for closest/most important entities. I'll take a look.
A couple things are planned: Town Hall - Lets you ring a warning bell to have all the non-militia go to it, and all the militia go to their Guard Posts. It will also provide some leadership stuff, but that's not really related to the alarm stuff. Guard Post - Where militia stand guard and patrol.
The idea of a safe room is cool. Maybe the town hall could have options to designate these.