Thank you for trying, but the problem persists. Doing a reboot, as you suggested, actually makes the problem worse: after the reboot the deviant behavior actually increases in speed and frequency.
I also tried visiting the Genius bar. Fortunately, I was able to show the technician a video of my iPad doing its crazy stuff before he ran the tests. If I understood him correctly, he said that my iPad's hardware was good, although not perfectly in order; he was fairly confident, however, that the problem was either connected with settings or with my Logitech case-with-bluetooth-keyboard. The technician then reset all the settings, and advised me to turn off the keyboard/bluetooth, using the mini for a few days without the keyboard to see if it would then be free of 'craziness'. I was at the Genius bar on Thursday 6 August and, sadly, the problems began to reoccur on Friday the 7th. Today, 9 August, the problems are worse (occurring faster and more persistently) than before.
I would like to attach a video here, but do not see how to do that (there is an active photo button here in my message header, but the video button is greyed out). In the video, the gremlin took over while I was reading in Mail, went to Safari and opened a website (one I had visited a few days previously). Then it gained control of the keyboard and started typing spontaneously. This is really quite alarming!
I feel that I am getting the run-around from both the point of sale (T-Online) and Apple. The mini is 18 months old so it is no longer guaranteed by Apple, although it is still under the 2-year warranty that is the European norm. The Genius at the bar said, that since I bought the mini through T-Online (our telephone service in Germany) I would have to take the mini back to point of sale to ask for a repair. Of course I had already been to the T-Online shop - they told me to go to the Apple genius bar.
This is all very upsetting, and what's worse, I will be travelling for the next two weeks and would normally be depending on my mini for email access and much more. Now I cannot depend on it. I feel like I'm in between a rock and a hard place.
If you have any more suggestions, please do let me know.