> I did not know about SMP or ASMP was proposed with Q Box.

SMP (as well as memory protection, resource tracking etc.) was the whole point of the QBox idea:

"The goal is to [...] work on a new OS layer using Quark functionality called Q-Box. [...] Because we believe that the original OS design has strong limits for newer technology through its design structure, we also plan a completly fresh and clean OS layer on top of the Quark kernel (called Q-Box now). The A-Box API [...] has serious limitations because it doesn't hide OS structures and has no concept of memory ownership. [...] As a consequence, we will not replicate the A-Box API in the Q-Box but we will try to do a new API without any compromises to the past but based on past experience."
http://web.archive.org/web/20020626181353/http://www.morphos.net/overview.php3

Regarding the "Quark functionality" to be used by the QBox, see there:

http://web.archive.org/web/20020626180435/http://www.morphos.net/kernelinfo.php3

> Can the A Box be placed inside the second core?

Yes, the Quark kernel running underneath both the ABox and any other potential box running in parallel with the ABox would be able to put the ABox on any core, and even switch between cores at runtime. That's the very nature of SMP after all.