Most of the suggestions you have made I am already aware of. I hadn't yet run Apple Diagnostics. I have done that now.
The only issue that the report identified was an issue with the battery. I don't believe that it is the battery that is the issue but the Magsafe to Magsafe 2 converter which I have to use to charge the battery. This has to be one of the most unreliable pieces of technology that Apple has ever produced. It's sole purpose is to narrow the width of the plug so that it will attach to the narrower Magsafe 2 connections installed in older MacBook Airs. However the converters seem to have a mean time to failure of about eighteen months, based on my experience. What happens is that one or more of the spring-loaded prongs no long springs out fully and as result the connection is no longer reliable. However, all that is by the way.
In my own attempts to troubleshoot the error messages, I have pinpointed the fact that the most common error message is fairly reliably produced when I log on to a particular online service. However, its appearance doesn't seem to be completely restricted to this situation. Also, I occasionally get other error messages that don't seem to be associated with that website. At present I'm focusing on that error message because, if I can discover what is causing it I may be able to work out what is causing it on the much less frequent occasions when it appears when I have not logged onto that website.
I have reported the issue to the owner of the website but I have been told that they have not received similar complaints from anyone else. The explanation for this could well be that most people are connecting to the service with PCs. Irrespective of whether or not that is true, one can scarcely expect a website administrator or an IT specialist to work out what the problem is if it is not possible to provide a clear explanation of the problem at the user end.
In this case, although an error message is generated, there is no obvious evidence of an error in transmission of information. It could be that the error message is of no practical consequence, beyond the irritation it causes. On the other hand it could be signalling that there is a nontrivial problem that is not obvious. That is why I have been keen to understand the nature of the error being reported.