Hi,
The fact that all Outgoing iMessages are marked "Not Delivered" as soon as you try to send them suggests you are not Logged in fully.
The other info suggests it might be the settings between the two devices but it is not entirely clear.
You don't say if you set up Text Forwarding (SMS) to the Mac and if these are part of the "messages" you talk about.
iMessages are the conversations where you sending an iMessages has Blue Bubble.
SMS ones are Green.
It is possible for the SMS Forwarding to still work even if iMessages syncing between the two does not.
Check these:-
On the Mac in Preferences > Accounts > iMessages account does it list in Receive At the Apple ID and iPhone Number ?
Are both Ticked to be active ?
If they are you should also have a "Start Conversation From" drop down that lists both as well.
Which one is selected ?
On the iPhone in Settings > Messages > Send and Receive does it list both the iPhone number and th Apple ID ?
Are both ticked to be active ? (The iPhone one should also be greyed out).
On this device which of the two is selected as the Send From item ?
On the Mac it is simple to tick inactive ones.
The iPhone may be more difficult if the iPhone number is the one Unticked.
If it is then Slide the Active item fro Messages to the Off position.
Then slide it On again and wait for the Number to verify (this can be a few minutes sometimes)
When that id done Add back the Apple ID.
Accept th pop ups on th Mac when you do this.
Is it syncing properly now ?
(Unfortunately it may not be).
Report back at this stage.
9:17 pm Wednesday; November 25, 2015
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad