Note that a reflexive relation has every object related to itself. An irreflexive relation has no object related to itself.
These three issues can be discussed together. We are likely to answer either yes to all or no to all, depending on whether we favour a stronger or weaker data model for SKOS semantic relations.
If we favour a stronger data model, then we answer yes to all three. The advantage is that we provide a stronger endorsement for checking consistency w.r.t. a model that (almost?) all thesauri, classification schemes and taxonomies adhere to. However, a stronger data model may close the door on some SKOS/OWL patterns.
If we favour a weaker data model, then we answer no to all three. The advantage is flexibility, which leaves the door open for certain patterns for using SKOS and OWL together (note that rdfs:subClassOf is reflexive).
SKOS Reference 2008-01-25, Section 7 (see especially notes 7.6.5, 7.6.7, 7.6.8)
ISSUE-80 (SKOS/OWL Patterns)
Thread starting from http://lists.w3.org/Archives/Public/public-swd-wg/2008Feb/0039.html