Hi Boleh,
>> 1) Deleted mails dont appear in Deleted items. I have checked the "Mark items for deletion.....
Theoretically, messages marked for deletion are displayed in strikethrough text and are not moved from their original folder. So this is an expected behavior that they won't appear in Deleted Items folder.
>> 2) Unchecking the box causes the deleted mail to appear in Deleted Items but will also appear in Inbox
I tested in my Outlook 2016 by clearing the checkboxes below and then right clicked an item in Inbox, clicked Delete, this item disappear from Inbox and showed up in Deleted Items folder as expected:

Did I misunderstand anything?
Could you please share more details about why you mentioned "Smartermail" in your post?
Any findings, please post back at ease.
Best regards,
Yuki Sun
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