It’s possible to make Dorico play anything you want, using the “add staff” workaround. Use Add staff, write the notes and rhythms you want for your turn, and hide (or delete) the added staff. Make sure you set the mute playback property on the appearing turn, so that Dorico only plays what’s hidden, and there you have it.
Yes unfortunately turns & mordents etc are not currently supported with playback, although I believe that is on their list of things to update in the future.
Here’s the page in the manual introducing the section on ornaments, with a note about expected playback (or lack thereof, in this case); this page is the 2nd result when searching “turn playback”
For showing accidentals either above or below ornaments like turns, see here:
For trills, the procedure is a bit different - see this page and the following set of pages for more info