The one in Mecca is the full haj, right? My colleague goes in
Oct every year for the umrah. Any particular “festival” in October
– I mean why does she pick that month?
Nopes. No idea. I believe that's her personal choice. In the
first place, the Islamic calendar is lunar, meaning that all dates
will shift back by 11 days per year - which is why you notice the
two Hari Rayas seem to get earlier and earlier each year.
Otherwise, Umrah can be performed at any time - my parents
performed it in June last year.