BT do not provide or maintain the external network. This is done by Openreach who work for all service providers. BT do not get any special treatment.
Thanks for the post and welcome to the forum. I am really sorry that the engineer didn't show and even more sorry that we did not keep you informed. It is not acceptable that we didn't let you know what was happening. I would like to help.
I cant promise that I will be able to improve on your next appointment date but I can promise that once we pick up your case we will own until full resolution and I am certain I can answer your questions. Please drop me an email, you will find the 'Mods contact link' under the 'About me' section of my profile. Just click on my username (SeanD).