Restore from Backup: Apps in iTunes library were not installed on iPhone because Unknown Error occurred 0xE800002D

After iPhone Restore from Backup & Sync causes iTunes Error Message:

I posted this weird copying behavior here:
Issues & Errors with Restore from ios7 Backup to ios9 on iPhone 5?

The screenshot of error message below is from this thread from Apple forums.

I get a similar looking error message, but with 200+ errors (as posted with details below):

So I split & posted this Error Message separately to solve this issue.

Some of the apps in your iTunes library were not installed on the iPhone “AS_iPhone5_711” because one or more errors occurred.
For a list of apps that could not be installed, click the + below.
..
The app “xxxx” was not installed on the iPhone “My_iPhone5_711” because an unknown error occurred (0xE800002D). // most apps have this error
..
The app “yyyy” was not installed on the iPhone “My_iPhone5_711” because an unknown error occurred (0xE800000E). // few apps, maybe only one or bit more

A few 'tries' of Restore from Backup & Sync, I observed some of the following behaviors:

• Sync is stuck for several Apps that are in a "funky" state:

  • On the iPhone: "Waiting" state:
    Folders & Apps all pending, semi grayed icons. Some with names visible others names 'waiting..'. If you clicked one its name would become 'waiting..'

  • On iTunes: Device > Apps view they were all "Will Install" state:
    But every time I sync apps don't install & the same flavor of errors come up

• For one app, when I upgraded the version via iTunes and it synced/ installed finally, but the rest did not work despite updates.

• It does not consistently 'funk' the same Apps. Once it was Viber, next time it was WhatsApp (and a lot of other apps, but the apps kind of changed)
  PS: I thought maybe it was AppSync causing it so I got rid of it last 2 'tries'.

• Most of these are legit & free purchased from AppStore

• Computer was also authorized via iTunes

I don't mind taking manual steps to resolve this as long as there is some way.

Found some posts that talk about this error, but they are old and not sure if connected.

Jun 06, 2013: https://discussions.apple.com/message/22259435#22259435
2011 - 2013/14: https://discussions.apple.com/thread/2765754?start=0&tstart=0

Try installing those bugged apps direct from the App Store, as opposed to relying on the backup package.

Use the backup to get your own content (photos, messages, etc), and ignore the apps. Download them fresh from the app store.