I use Linux+Qt and some themes simply does not implement bevel around group box (for example a new theme Breeze from Plasma5).
Try to change your GTk theme, maybe bevel will appear.
For compiling Lazarus with Qt, you need libQt4pas.so. Try to install it from Mint repositories. If it is not there, download it from here:
http://users.telenet.be/Jan.Van.hijfte/qtforfpc/fpcqt4.htmlCopy the file to /usr/lib (or where Mint has libraries) and also create version symlinks:
file: /usr/lib64/libQt4Pas.so.5.2.5
link: /usr/lib64/libQt4Pas.so.5.2
link: /usr/lib64/libQt4Pas.so.5
link: /usr/lib64/libQt4Pas.so
Then run
ldconfig as a superuser.
Finally, set Qt in the "Configure Build dialog" and rebuild Lazarus.