Some good advice from others.
I've recently switched to fibre and I was told the old copper landline was being removed, so that might not be a fall back option. When you said the engineer that installed it ran an extension off your old phone socket, are you saying he didnt run new cable from the nearest pole/box to your house? If not, did you have fibre to the house before?
Also, the answer to question 1 in your original post is no. If its an Openreach issue then changing providers wont make any difference.