Given he doesn't explain to Chu Shuzhi what to do, this makes me wonder if the SID has safe houses in other cities, and what they might be used for.

I wondered about this, too, when I was typing up notes for the post.

I remember the first time I watched this scene, I fully expected Lin Jing's eavesdropping device to reveal Shen Wei's identity

I thought the same thing. This time, I watched carefully and we never clearly see when Lin Jing puts the listening device away.