As stated in a previous post, via redundancy is the requirement to add a second, redundant via wherever possible (sometimes there is not enough room to add a second via). The reason is to improve functional yield by making the design more tolerant of via failures. Also it reduces the current through the via (also good for reliability) and reduces the resistance of the contact.
I don't know where you got the term "island", it is very vague. I am guessing you mean "metal island" or metal fill island". Metal fill is the set of floating "islands" of metal that are inserted wherever there is open space without any (or enough) routing wires. The reason is to improve manufacturability. If you do not add metal fill in these areas then the the chemical-mechanical polishing (CMP) step during manufacturing will abrade away the oxide more quickly in these places than in places where there is a lot of metal. This is called "dishing" and leads to degraded planarity of the layers.
In older processes the metal fill was implemented as wires connected to power or ground. This is not done anymore and floating "islands" of metal are used instead.