Sorry for the delay but I did not wish to spoil your weekend! It also gave me some more time to fiddle with the settings.
Answers to your questions, in reverse order:
I can assure you that you'll not find bread crumbs in my keypads or greasy fingerprints on my screens: there are no visible signs of dust or dirt to block the buttons.
I did not reset the base unit to factory settings yet, so as not to loose my directory (I will do it as a last measure, if required). However, I've reset both the base handset and the remote handset: in fact, I've swapped them, renaming both. Now, the announcements continue but only now and then; they do not wake me up at night any more.
The messages are audible on the base set which is on my desk, I cannot say if they are on the extension as well.
I am now going to switch off all my WiFi connections for a day or so in case there are responsible for an interference. If so, I can get rf absorber cylinders and fit them on the power and telephone lines.
I found a Samsung answer telephone in my basement: it worked with no problems but I am not keen on installing it for good as I do like the look and feel of the old Gigaset C475.
Yes, I did disconnect/reconnect the mains.
Your suggestions, please.