What do they primarily read in synagogue worship?

In synagogue worship, they primarily read from the Torah, from Moses. The Law of Moses is read, but a veil remains on their hearts so they cannot see that it has passed off the scene. This is their sincere practice.

Les explains that in synagogue worship, the primary reading is from the Torah, from Moses. He notes Paul wrote this around 60 A.D., but the same truth applies to 1997. The Jewish people are sincere, and Paul felt the same toward them, yet as they read the Law of Moses, the veil remains on their heart, preventing them from seeing that the Law has passed off the scene. Les then points to Romans chapter 11 as a plainer explanation.

2 Corinthians 3:15

But even unto this day, when Moses is read, the vail is upon their heart.

Are Jewish people sincere in reading the Law, and what happens to them when the Torah is read?

Yes, the context describes them as sincere in their activity, and Paul felt the same toward them. Yet when Moses or the Torah is read in synagogue worship, the veil remains upon their heart, keeping them from seeing that the Law has come to an end and something better has replaced it.