Can I run Ubuntu applications in Xubuntu? Are there any problems doing so? Can GNOME applications run in XFCE-based systems?
Yes, both Ubuntu and Xubuntu use same repository. So, you can install and use gnome applications such as gnome-terminal in Xubuntu. But mind it, you can't use gnome-session in Xubuntu.
I myself used Xubuntu with gnome or Ubuntu applications, such as gnome-terminal, gedit etc. It's perfectly ok, unless you tried to run gnome or Ubuntu sessions on top of Xubuntu session.
Comment by the OP:
Yes, of course. As long you installed the gtk libraries and necessary development tools.