No, everything is mostly open on Sunday.

Saturday night, which is when the 9th of Av actually started, most (but not all) things were closed, but Sunday everything is open again, especially businesses.

Jewish Holidays go by the Hebrew Calendar, which counts days from Night to Night, not from Sunrise to Sunrise. So when the regular calendar says that the 9th of Av is on Sunday, the actual holiday is the evening of Saturday, then Sunday 'til evening.

9th of Av is less observed in general Israeli society, compared to other occasions. Other occasions (i.e. Jom kippur, shavuot) all/most (depends on the occasion) businesses would be closed, but not on 9th of Av.