We will be staying near La Merced. What eating options would we have between 10- 11 PM ?
Slim pickins at that hour. Right at ten you might be okay. Friday or Saturday you should be okay. Wednesday at 11 PM you are pretty much SOL, although there is always the street food on Santa Lucía.
Yes, in my experience (I often arrive late, stay in the same neighborhood, will be doing so next month again) there's not much on offer. Even the street venders at La Merced have usually gone to bed by then. There might be a bar sort of spot on 5 Avenida still open that would serve food. I generally layover at IAH or DFW, eat there, and buy some fruit for later. Or buy food on the plane.
Fridas on fifth ave should still be open and serving food. It's a bar atmosphere though. It's half a block from la Merced. Cafe Rocio on sixth ave may still be open serving curries. Depends on what night you're arriving also. Probably better luck on Friday and Saturday.
It will be a Tuesday night. To avoid the bar/ noise after a long day, I think Frida's has take out. Could be the answer.
I would be shocked if they are open that late but you never know. Frida's hours and menu and almost everything about the place could be described as extremely flexible.