  The orbifold braid groups of two dimensional orbifolds were defined in [1]
(arXiv:math/9907194) to understand certain Artin groups as subgroups of some
suitable orbifold braid groups.
  We studied orbifold braid groups in some more detail in [17]
(arXiv:2006.07106) and [18] (arXiv:2106.08110), to prove the Farrell-Jones
Isomorphism conjecture for orbifold braid groups and as a consequence for some
Artin groups. In this article we apply the results from [17] and [18], to study
two aspects of the orbifold braid groups. First we show that the homomorphisms
induced on the orbifold braid groups by the inclusion maps of a generic class
of sub-orbifolds of an orbifold are injective.
  Then, we prove that the centers of most of the orbifold braid groups are
trivial.
