Thanks for your suggestions.
1. I deleted and recreated the accounts but still not working. I really like to use is as I am using very often one of the templates. If you have any other suggestions, please let me know.
2. So far I never sent photos directly from 'mail'. I am really glad you told me. I discovered something new and for sure some of the templates I plan to use very often.
I just like to let you know the problem is fixed. At the end I did not have to call tech support.
This worked for me:
Preferences on Mail - Accounts - Account Information - Outgoing mail server : change to icloud & use this server only.
Before that I also recreated all the mail accounts. Maybe this has something to do with it as well but at least it worked.