What version of wxGTK are you using? What GTK2/3 theme are you using? Can you try the auidemo from the wxGTK project if it has the same problems?
I have not yet installed wxWidgets other than via $ sudo apt-get install codeblocks*
If I search I find files like /usr/lib/x86_64-linux-gnu/libwx_gtk2u_aui-3.0.so.0.2.0
I guess that means GTK2?
I am using the default desktop theme under kubuntu, this is a fresh OS installation I am just trying to configure it. In the system settings the "look and feel is "Breeze" and Desktop Theme is also "Breeze"
It should be said when I check my old computer with Kubuntu 15.10 the tooltip problem is the same in Code::Blocks there. I have not been able to compile anything on the new computer yet, but on the old one I can confirm the tooltip problem was also the same there. So this isn't new.
The toolbar size problem has become worse though. I can see the problem relates to toolbars with comboboxes especially, but even the other ones have "too much air". I have Windows and Kubuntu side by side with identical screens and both with codeblocks, the toolbars are wasiting several cm vertically compared to on Windows unless I keep only one row of toolbars, but this isn't optimal.