Most of these questions are quickly answered by either referring to the Solr Wiki or to a web search, but to get the gist of DocValues: they're useful for all the other stuff associated with a modern Search service except for the actual searching. From the Solr Community Wiki:
DocValues are a way of recording field values internally that is more efficient for some purposes, such as sorting and faceting, than traditional indexing.
...
DocValue fields are now column-oriented fields with a document-to-value mapping built at index time. This approach promises to relieve some of the memory requirements of the fieldCache and make lookups for faceting, sorting, and grouping much faster.
This should also answer why Lucene 5 requires DocValues for sorting - it's a lot more efficient than the previous approach.
The reason for this is that the storage format is turned around from the standard format when gathering data for these operations, where the application previously have to go through each document to find the values, it can now look up the values and find the corresponding documents instead. Which is very useful when you already have a list of documents that you need to perform an intersection on.
If I remember correctly, updating a DocValue-based field involves yanking the document out from the previous token list, and then re-inserting it into the new location, compared to the previous approach where it would change loads of dependencies (and reindexing was the only viable strategy).
Use DocValues for fields that need any of the properties mentioned above, such as sorting / faceting / etc.
