Hello Nadav
Anycast can indeed provide redundancy. With the growth of the Internet, many network services are using Anycast for high-availability requirements, such as DNS and content delivery networks. Anycast has grown in popularity for this purpose.
Closest could mean multiple things. It could be on the basis of number of hops, physical distance, lowest cost based on a metric, latency, or based on the least congested route. Content delivery systems like Netflix may use it in order to have users obtain content from the closest possible (and thus fastest and least costly) server. This essentially brings the content closer to the end user.
Only if there is a fault in configuration. IPv6 routers on the path of an Anycast packet through the network will not distinguish it from a unicast packet, but special handling is required from the routers near the destination (that is, within the scope of the Anycast address) as they are required to route an Anycast packet to the “nearest” interface within that scope. This is determined in much the same way that a routing protocol determines the path to a specific destination, based on whatever measure of distance (hops, cost, etc.) is being used.
I hope this has been helpful!
Laz