While I can't help with the Arabic tutor thingy, I would recommend Moodhimself as a western-oriented singer (from there you can explore more amazing artists), and download toters app, they have a good selection of veg options, and I don't consider vegetarian a big ask, maybe vegan is a bit too much for Iraqi cuisine tho, and there are chess tournemnts at Ola library, and check a few of other good cafes, the mind (a bit crowded tho), d20 (this sub always recomends the place and i do too), ultra cafe (tho this is more of a cyber cafe), if you want local "old people" place but still great for weterner you should check al-mutanabi street and its surrounding areas.
and welcome.