Once you've set up Family Sharing, everyone can access each others' apps, music, movies, TV shows and books.
To download content from another family member, sign into your iTunes account and visit the "Purchased" pages in the iTunes store, iBook store or App Store. Simply choose the family member whose content you want, and go ahead and download.
I also shared my Apple ID with my wife for app purchases, and found the transition to Family Sharing painless. This Apple support page goes into details, and I'll answer some of your specific questions below.
What will happen to her existing apps, some of which have saved local data?
Most likely your wife's iPhone is set up so that iCloud (Settings > iCloud) is using B's Apple ID, and iTunes & App Store (Settings > iTunes & App Store) is set up with A's Apple ID. This makes the transition easy, but just in case please make a full encrypted backup with iTunes.
On your wife's iPhone, go to Settings > iTunes & App Store > Apple ID and click "Sign Out", reboot the iPhone, and then sign in with your B's Apple ID. A should then create the family group and invite B to the group.
The existing apps might still be marked as "purchased by" A. If my wife wants to update them, she'd need to enter the A credentials
The linked answer describes how app authentication works when there are apps purchased under multiple Apple IDs on the same device. The authentication process for Family Sharing works differently.
Under Family Sharing, account B's credentials will be valid for purchases shared by other family members if she has been flagged as a Parent/Guardian by the Family Organizer. This includes apps, music, movies, and iBooks. To download apps made by other members, open the store app that you want to download content from, and go to the purchased page. On iOS devices this is located at:
App Store: Tap Updates > Purchased.
iTunes Store: Tap More > Purchased.
iBooks: Tap Purchased.
The only time that a purchase needs to be authenticated is when a child that has be set as "Ask to Buy" tries to make a purchase.
Best Answer
Sure you can.
You can set your preferred account as Organiser, with Share my purchases switched on, then invite & add your other account as an Adult (you could set yourself up as a child, but then you'd have to ask yourself permission ;)
From System prefs > iCloud > Manage Family...
First & last are 'me'
One caveat - you need to make sure that the two addresses aren't already associated. I had great difficulty figuring out why adding my second account wouldn't work. It turned out to be [iirc] that each was using the other as the rescue or secondary email address.
As you're setting it up initially you need two devices [or accounts on a Mac] each to be signed into its own account. It took some juggling for me to set this up on a single Mac, but between iPhone & Mac ought to be simpler.
Full setup details at Apple KB: Set up Family Sharing
I'm not sure whether doing this will enable the right to the Mac version of an iOS app. It usually wouldn't, but the iWork suite & Apple's own software in general seems a bit of a special case.