My site is now https!
I was probably the last in line to make the switch, but just in case:
If it doesn´t work as supposed the first time you switched, just switch it back and do it again.
For me, the first time around it didn´t work and I got the encircled ¨i¨ instead of the green safety lock. Consequently, I went through lots blogs and others´ questions about it and tried out a number of things. All to no avail.
I even had to get site support to deactivate a couple related plugs as I couldn´t get into my site anymore.
In reply to my question, Kyle said certain things should change all by themselves.
Then I decided to put the htttp back and refreshed the site. After this, I switched back to https and low and behold, the green lock showed and my site secure.
So, yes, this is how simple problem solution can be sometimes.
Have a pleasant day,