Your use of core in these examples refers to the meaning as in the earth's core. Right inside.
We can have core beliefs but we do not say core of the city (city centre is the usual). Core of experts is acceptable but more natural would be group of experts; core curriculum is correct, being that part of the curriculum that is central and essential. Core time? Maybe, but as business usage can mangle our normal usage then anything is possible. Your suggestion seems to fit quite well.
Student or Learner