I just wanted to get more information on the search bar and couldn’t get any more details. For me there is no “Fragezeichen” in the search bar.
I especially wanted to look for filetypes.
DEVONthink To Go doesn’t support searching by filetypes specifically. You may find matches with a construct like Name:.docx.
I am not seeing any issue with the lack of question mark in the search field in our internal build.
Also, the search is covered in the ? > Help > Appendix > Search Operators.
That’s interesting; I just opened DTTG on my iPhone to find the ? missing from the search bar. On quitting DTTG and re-opening, the ? was back again. I’ve never noticed this before, I’ll keep an eye open for the behaviour.
Yes, if you find any consistently reproducible steps, let us know.
I’m not seeing any issue when accessing the search field from the Home screen or within a database.
Noted as a feature request 
So should there be a “Fragezeichen” in the search bar or not? If not then the help text should be adapted.
Yes there should, and generally there is; as I mentioned, I found the ? to be missing too - it returned when I restarted DTTG. Have you tried that?