Though the interface of V2 is a bit different, almost all the things you've asked for can already easily be done on V2.
When you view a collector's profile, there are options to match with you collection by selecting All (to view all the cards in one list) or Companies (see the matching companies).
Items recently added to the catalog will be available soon when new updates arrive. There will not be new updates to the catalog for at least a week to help stabilize V2 before making more changes.
To search collectors by country you should click Countries in Collectors page.
Updating your collection is the same as before, just no more need for "Update Collection" button. When you check an item, it's added to the list. When you uncheck it, it's removed. Much simpler than before.