Hi,
I would double check the settings.
You seem to be listing several devices listing the Apple ID but none of them seem to be getting the SMS forwarded to them.
The way it can be done is Start en Messages App on the iPhone (It can do iMessages from the iPhone Number)
You can enable SMS as well (it will now do both)
Add an Apple ID to the Mac version. (It can now send from the Apple ID)
You can test to the iPhone by manually typing in the iPhone Number including Country Code.
Send an iMessage.
If it works add the Apple ID in the Send and Receive setting on the iPhone.
Accept the pop up on the Mac.
Both devices can now Send and Receive on both iPhone Number and Apple ID.
Make sure the iPhone is on the same LAN as the Mac(s) or iOS devices using the Apple ID.
Enable Text Forwarding.
This looks similar to Blue Tooth pairing but it is not and uses the LAN to link the two (at the set up stage) devices.
You should be able to Pair to one of the Macs.
That Mac will get SMS after you see the Code and enter it back on the iPhone.
Repeat where required for other Macs an iOS devices using the Apple ID
The most often missed part is making sure all devices are on the same LAN.
If you have added a range extender that routes then they should all be in the same SubNet.
If you are getting SMS but not iMessages then the Mac is not logged in to the iMessage Server properly.
IF you are getting iMessages but not SMS then either iPhone is not doing SMS or the link is not working. Re-set Text Forwarding.
Partial SMS (Receiving but not Sending) does seem a bit weird.
I would look to the Carrier service dropping out mid conversation as it the bit the iPhone And the Mac use and is also probably the least stable in some areas.

7:50 pm Sunday; December 10, 2017
iMac 2.5Ghz i5 2011 (Sierra)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone 6 iOS 11.x and an iPad (2)