Your understanding is correct. To answer your questions:
No - using prefix list tells the peer you can deliver packets to ALL of the networks you advertise 1.1.1/22 which I suppose would be incorrect, so you could potentially black hole traffic if you cannot deliver, Aggregate route on the other hand allows you to advertise the whole subnet as indicated but deliver only to the ones you can deliver and send a reject/discard those you cannot deliver. Now in addition to reducing the size of the peer you are advertising the agg route to, you also hide instabilitiexs internally and reduce the likelyhood of flapping when a route goes down.
Another use case that aggregate routes are typically used, on Border routers for advertising a default route in the reverse direction, i.e. into the IGP domain. So that if the Border router does not have internet connectivity, based on not receiving a contributing route from the peer, then the default route will not become active and is not advertised so the internal routers will find a different route to remote destinations.