My problem has just happened again, and with a bit more experimentation I understand a little more about it, although I am still puzzled.
As usual, I clicked on one of the FS links from RM’s people page and again found RM hanging. I then checked FS in my browser to see whether I was logged on, and found that I could not access it. I could access all other internet pages I tried, but sites like down detector indicated that FS was up and running. The problem was not with my PC, because I couldn’t access FS from my phone either. However, if I switched my phone’s wifi connection off and relied on its 4G network link, I could get to FS. Something is plainly intermittently wrong with my router (although re-starting that doesn’t seem to work) or my ISP.
Anyway, when I set up a hot spot connection to allow my PC to connect to the internet via my phone’s 4G network, I could open FS in my PC’s browser and log on. At this point, RM was still hanging, but when I closed the screen, it did not become un-responsive as before, and on re-trying, I could open the FamilySearch Person Tools page in FS and see the data.
I then switched the hotspot connection off, and reverted to using my wifi connection/ISP. As before, I couldn’t open the FS web page, but much to my surprise, I could continue to use the FamilySearch Person Tools page to view more data from FS.
After a while, however, FS once again seized up and once again did not open properly after I had closed it from the task manager. It eventually did open properly after I had reconnected my PC to my phone’s 4G connection, although I don’t know whether this was a factor or not.
So it seems that there are two separate problems, an intermittent problem in either my router or ISP’s connection to FamilySearch which I will have to investigate further, and a problem with RM when the connection to FS is not working. FS does not time out as it should, and worse still it doesn’t start cleanly when it is re-opened.
Edit a little later: FamilySearch will now open in my PC’s browser through my wifi and ISP as usual. I am no closer to finding out why it wouldn’t open earlier.