Firstly, 9eme is close to 1ere, I'd say only about 15-20min walk.
Korcarz on Rue des Rosiers on 4eme has a side area where you can sit down.

I would have recommended Baan Hai on 1eme but I heard they closed down.
There's Casa Rina but i thought they're dairy. There's also one or two small sushi place, I'll post if I can remember the names.