Where can I find a part time job only on Fridays and Saturdays?
Look for jobs on OpenSooq.com or Tanqeeb you might find what you are looking for
Where can I find a study lounge near cozmo?
@Caribou Cafe in Barakah mall its a bit far but I go there to study sometimes :)
Where can I find a spa point with a female therapist?
@The Spa in Four Seasons they have the greatest service, you should defiantly go there
Where can I find a running club?
There aren't many in Amman but there's one group on Facebook named "Right To Movement" look for it and join they post the times for runs and such, good luck!
Where can I have professional business writing and communication skills courses?
@Modern Language Center has an business writing course, some of the teachers are native speakers so you might get a great experience there! good luck!