I can confirm #1 is legit issue.
I build a "What do the components look like on Windows, Linux and Mac"... included everything from Standard, Addition, Common, Misc, and Laz.
TDateEdit, when you click the Calendar Button - the Calendar renders with correct information. Click, DblClick, Enter, nothing will make the popup Calendar close and return the selected date.
Now, TDateTimePicker, when you click on the dropdown to see the Calendar, the Calendar flashes up and closes instantly.
This same project runs on Windows and Linux without issue.