Yes to all haha. Entities will walk into cages (even more likely if their dietary foods are in it) and get stuck. Then you assign the capture job to the cage and there's a chance to capture them (higher with a high animal husbandry skill). When captured, sentient creatures can be integrated as citizens. This will unlock their research tree and events.
Green arrow up means they can climb upwards from that block.
Blue arrow down means they can climb downwards from that block.